Elliptic curve isogeny class with Cremona label 100188c (LMFDB label 100188.k)

• Label: 100188c
• Number of curves: $1$
• Conductor: $100188$
• CM: no
• Rank: $1$

Rank

The elliptic curve 100188c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 100188c do not have complex multiplication.

Modular form 100188.2.a.c

Elliptic curves in class 100188c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100188.k1	100188c1	\([0, 0, 0, -6400053, 6231942981]\)	\(-51964534050048/253\)	\(-141152283139824\)	\([]\)	\(1105920\)	\(2.3368\)	\(\Gamma_0(N)\)-optimal