WeierstrassInvariantG3

WeierstrassInvariantG3[{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  (3)

Evaluate to high precision:

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

TraditionalForm formatting:

Applications  (1)

Define the discriminant of the Weierstrass elliptic curve:

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

Compare with the builtin function value:

Wolfram Research (2017), WeierstrassInvariantG3, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html.

Text

Wolfram Research (2017), WeierstrassInvariantG3, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html.

BibTeX

@misc{reference.wolfram_2021_weierstrassinvariantg3, author="Wolfram Research", title="{WeierstrassInvariantG3}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html}", note=[Accessed: 17-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_weierstrassinvariantg3, organization={Wolfram Research}, title={WeierstrassInvariantG3}, year={2017}, url={https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html}, note=[Accessed: 17-October-2021 ]}

CMS

Wolfram Language. 2017. "WeierstrassInvariantG3." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html.

APA

Wolfram Language. (2017). WeierstrassInvariantG3. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html