Elliptic curve isogeny class with LMFDB label 29157.a (Cremona label 29157b)

• Label: 29157.a
• Number of curves: $1$
• Conductor: $29157$
• CM: no
• Rank: $3$

Rank

The elliptic curve 29157.a1 has rank \(3\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(9719\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29157.a do not have complex multiplication.

Modular form 29157.2.a.a

Elliptic curves in class 29157.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29157.a1	29157b1	\([0, 1, 1, -240, 1190]\)	\(1535202758656/191299077\)	\(191299077\)	\([]\)	\(54864\)	\(0.31880\)	\(\Gamma_0(N)\)-optimal