Elliptic curve isogeny class with LMFDB label 306128.m (Cremona label 306128m)

• Label: 306128.m
• Number of curves: $1$
• Conductor: $306128$
• CM: no
• Rank: $0$

Rank

The elliptic curve 306128.m1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(19\)	\(1\)
\(53\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 306128.m do not have complex multiplication.

Modular form 306128.2.a.m

Elliptic curves in class 306128.m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
306128.m1	306128m1	\([0, 0, 0, 352336, -45982736]\)	\(25102282752/19266931\)	\(-3712736227578720256\)	\([]\)	\(3974400\)	\(2.2513\)	\(\Gamma_0(N)\)-optimal