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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 80688.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80688.j1 | 80688a1 | \([0, -1, 0, 308744, -117631088]\) | \(334568302/807003\) | \(-7850697467493832704\) | \([]\) | \(1451520\) | \(2.3095\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80688.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80688.j do not have complex multiplication.Modular form 80688.2.a.j
sage: E.q_eigenform(10)