Elliptic curve isogeny class with Cremona label 291312by (LMFDB label 291312.by)

• Label: 291312by
• Number of curves: $1$
• Conductor: $291312$
• CM: no
• Rank: $2$

Rank

The elliptic curve 291312by1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 291312by do not have complex multiplication.

Modular form 291312.2.a.by

Elliptic curves in class 291312by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
291312.by1	291312by1	\([0, 0, 0, -250563, 2143649986]\)	\(-83521/95256\)	\(-1984134862164476657664\)	\([]\)	\(14100480\)	\(2.7656\)	\(\Gamma_0(N)\)-optimal