Elliptic curve isogeny class with LMFDB label 19800.r (Cremona label 19800g)

• Label: 19800.r
• Number of curves: $1$
• Conductor: $19800$
• CM: no
• Rank: $1$

Rank

The elliptic curve 19800.r1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 19800.r do not have complex multiplication.

Modular form 19800.2.a.r

Elliptic curves in class 19800.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19800.r1	19800g1	\([0, 0, 0, 285, 118190]\)	\(137180/323433\)	\(-6036036019200\)	\([]\)	\(23040\)	\(1.1314\)	\(\Gamma_0(N)\)-optimal