Elliptic curve isogeny class with Cremona label 3185e (LMFDB label 3185.i)

• Label: 3185e
• Number of curves: $1$
• Conductor: $3185$
• CM: no
• Rank: $0$

Rank

The elliptic curve 3185e1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3185e do not have complex multiplication.

Modular form 3185.2.a.e

Elliptic curves in class 3185e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3185.i1	3185e1	\([1, -1, 0, 236, 16673]\)	\(251559/21125\)	\(-121781421125\)	\([]\)	\(5040\)	\(0.80662\)	\(\Gamma_0(N)\)-optimal