Elliptic curve isogeny class with LMFDB label 4446.e (Cremona label 4446g)

• Label: 4446.e
• Number of curves: $1$
• Conductor: $4446$
• CM: no
• Rank: $1$

Rank

The elliptic curve 4446.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4446.e do not have complex multiplication.

Modular form 4446.2.a.e

Elliptic curves in class 4446.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4446.e1	4446g1	\([1, -1, 0, -9009, -343139]\)	\(-110931033861649/6497214464\)	\(-4736469344256\)	\([]\)	\(9360\)	\(1.1882\)	\(\Gamma_0(N)\)-optimal