WeierstrassInvariantG2

WeierstrassInvariantG2[{ω,ω}]

gives the invariant for the Weierstrass elliptic functions corresponding to the halfperiods {ω,ω}.

Details

Examples

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Basic Examples  (2)

Evaluate numerically:

Plot the invariant:

Scope  (6)

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate symbolically for the equianharmonic case:

Evaluate symbolically for the lemniscatic case:

WeierstrassInvariantG2 has both singularities and discontinuities:

WeierstrassInvariantG2 can be used with CenteredInterval objects:

TraditionalForm formatting:

Applications  (1)

Define the discriminant of the Weierstrass elliptic curve:

KleinInvariantJ can be expressed as the ratio of a power of the invariant and the discriminant:

Compare with the builtin function value:

Wolfram Research (2017), WeierstrassInvariantG2, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassInvariantG2.html (updated 2023).

Text

Wolfram Research (2017), WeierstrassInvariantG2, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassInvariantG2.html (updated 2023).

CMS

Wolfram Language. 2017. "WeierstrassInvariantG2." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/WeierstrassInvariantG2.html.

APA

Wolfram Language. (2017). WeierstrassInvariantG2. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassInvariantG2.html

BibTeX

@misc{reference.wolfram_2023_weierstrassinvariantg2, author="Wolfram Research", title="{WeierstrassInvariantG2}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassInvariantG2.html}", note=[Accessed: 13-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_weierstrassinvariantg2, organization={Wolfram Research}, title={WeierstrassInvariantG2}, year={2023}, url={https://reference.wolfram.com/language/ref/WeierstrassInvariantG2.html}, note=[Accessed: 13-April-2024 ]}