Elliptic curve isogeny class with LMFDB label 3185.a (Cremona label 3185g)

• Label: 3185.a
• Number of curves: $1$
• Conductor: $3185$
• CM: no
• Rank: $1$

Rank

The elliptic curve 3185.a1 has rank \(1\).

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
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 3185.2.a.a

Elliptic curves in class 3185.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3185.a1	3185g1	\([1, -1, 1, -246357, 47126706]\)	\(-688691336801860161/8251953125\)	\(-19812939453125\)	\([]\)	\(29040\)	\(1.7007\)	\(\Gamma_0(N)\)-optimal