Elliptic curve isogeny class with Cremona label 100011e (LMFDB label 100011.a)

• Label: 100011e
• Number of curves: $1$
• Conductor: $100011$
• CM: no
• Rank: $1$

Rank

The elliptic curve 100011e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(17\)	\(1 - T\)
\(37\)	\(1 - T\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 100011e do not have complex multiplication.

Modular form 100011.2.a.e

Elliptic curves in class 100011e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100011.a1	100011e1	\([0, 1, 1, 1070, 7408]\)	\(135353378115584/99811078011\)	\(-99811078011\)	\([]\)	\(121968\)	\(0.79881\)	\(\Gamma_0(N)\)-optimal