Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 137904.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
137904.by1 | 137904f1 | \([0, 1, 0, -69, -909]\) | \(-53248/459\) | \(-317730816\) | \([]\) | \(60480\) | \(0.31402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 137904.by1 has rank \(0\).
Complex multiplication
The elliptic curves in class 137904.by do not have complex multiplication.Modular form 137904.2.a.by
sage: E.q_eigenform(10)