Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1600.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1600.b1 | 1600y1 | \([0, 0, 0, 500, 10000]\) | \(270\) | \(-51200000000\) | \([]\) | \(1920\) | \(0.73777\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1600.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1600.b do not have complex multiplication.Modular form 1600.2.a.b
sage: E.q_eigenform(10)