Elliptic curve isogeny class with Cremona label 51376a (LMFDB label 51376.q)

• Label: 51376a
• Number of curves: $1$
• Conductor: $51376$
• CM: no
• Rank: $1$

Rank

The elliptic curve 51376a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51376a do not have complex multiplication.

Modular form 51376.2.a.a

Elliptic curves in class 51376a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51376.q1	51376a1	\([0, 0, 0, -3056027, -2066616838]\)	\(-22359484836/130321\)	\(-18397037072643613696\)	\([]\)	\(938496\)	\(2.5375\)	\(\Gamma_0(N)\)-optimal