Elliptic curve isogeny class with LMFDB label 32634.z (Cremona label 32634c)

• Label: 32634.z
• Number of curves: $1$
• Conductor: $32634$
• CM: no
• Rank: $0$

Rank

The elliptic curve 32634.z1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32634.z do not have complex multiplication.

Modular form 32634.2.a.z

Elliptic curves in class 32634.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32634.z1	32634c1	\([1, -1, 0, -999609, 385105517]\)	\(-139072344741/75776\)	\(-60187364809721856\)	\([]\)	\(354816\)	\(2.1683\)	\(\Gamma_0(N)\)-optimal