Elliptic curve isogeny class with LMFDB label 312050.o (Cremona label 312050o)

• Label: 312050.o
• Number of curves: $1$
• Conductor: $312050$
• CM: no
• Rank: $0$

Rank

The elliptic curve 312050.o1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(79\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 312050.o do not have complex multiplication.

Modular form 312050.2.a.o

Elliptic curves in class 312050.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
312050.o1	312050o1	\([1, 1, 1, -171396713, 864272502231]\)	\(-3665123505412225/3272081408\)	\(-497126214830181908480000\)	\([]\)	\(54063360\)	\(3.4718\)	\(\Gamma_0(N)\)-optimal