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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 428736ex
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 428736.ex1 | 428736ex1 | \([0, 1, 0, -152097, -22907841]\) | \(-1484391946907017/1946200179\) | \(-510184699723776\) | \([]\) | \(3072000\) | \(1.7290\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 428736ex1 has rank \(0\).
Complex multiplication
The elliptic curves in class 428736ex do not have complex multiplication.Modular form 428736.2.a.ex
sage: E.q_eigenform(10)