Elliptic curve isogeny class with Cremona label 209814cm (LMFDB label 209814.e)

• Label: 209814cm
• Number of curves: $1$
• Conductor: $209814$
• CM: no
• Rank: $2$

Rank

The elliptic curve 209814cm1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(11\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 209814cm do not have complex multiplication.

Modular form 209814.2.a.cm

Elliptic curves in class 209814cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
209814.e1	209814cm1	\([1, 1, 0, 1329, 183429]\)	\(506447/28512\)	\(-14597605950048\)	\([]\)	\(518400\)	\(1.2057\)	\(\Gamma_0(N)\)-optimal