Elliptic curve isogeny class with LMFDB label 416.a (Cremona label 416b)

• Label: 416.a
• Number of curves: $1$
• Conductor: $416$
• CM: no
• Rank: $1$

Rank

The elliptic curve 416.a1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 416.a do not have complex multiplication.

Modular form 416.2.a.a

Isogeny graph

Elliptic curves in class 416.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
416.a1	416b1	\([0, -1, 0, 0, 4]\)	\(-8/13\)	\(-6656\)	\([]\)	\(16\)	\(-0.58741\)	\(\Gamma_0(N)\)-optimal