Elliptic curve isogeny class with Cremona label 109200c (LMFDB label 109200.m)

• Label: 109200c
• Number of curves: $1$
• Conductor: $109200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 109200c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 109200c do not have complex multiplication.

Modular form 109200.2.a.c

Elliptic curves in class 109200c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
109200.m1	109200c1	\([0, -1, 0, -7288, -557993]\)	\(-107040567189760/277254364023\)	\(-110901745609200\)	\([]\)	\(290304\)	\(1.3826\)	\(\Gamma_0(N)\)-optimal