Elliptic curve isogeny class with LMFDB label 337896.w (Cremona label 337896w)

• Label: 337896.w
• Number of curves: $1$
• Conductor: $337896$
• CM: no
• Rank: $1$

Rank

The elliptic curve 337896.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 337896.w do not have complex multiplication.

Modular form 337896.2.a.w

Elliptic curves in class 337896.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
337896.w1	337896w1	\([0, 0, 0, -27075, -1803917]\)	\(-4000000/247\)	\(-135539559528048\)	\([]\)	\(691200\)	\(1.4661\)	\(\Gamma_0(N)\)-optimal