Elliptic curve isogeny class with Cremona label 997b (LMFDB label 997.c)

• Label: 997b
• Number of curves: $1$
• Conductor: $997$
• CM: no
• Rank: $2$

Elliptic curves in class 997b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
997.c1	997b1	\([0, -1, 1, -5, -3]\)	\(16777216/997\)	\(997\)	\([]\)	\(48\)	\(-0.67163\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curve 997b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 997b do not have complex multiplication.

Modular form 997.2.a.b