Elliptic curve isogeny class with LMFDB label 688.b (Cremona label 688c)

• Label: 688.b
• Number of curves: $1$
• Conductor: $688$
• CM: no
• Rank: $1$

Elliptic curves in class 688.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
688.b1	688c1	\([0, -1, 0, -5, -19]\)	\(-4096/43\)	\(-176128\)	\([]\)	\(80\)	\(-0.31128\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curve 688.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 688.b do not have complex multiplication.

Modular form 688.2.a.b