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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 36784w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36784.f1 | 36784w1 | \([0, 1, 0, -2581, -51537]\) | \(-4194304/19\) | \(-8616872704\) | \([]\) | \(28560\) | \(0.75802\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 36784w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 36784w do not have complex multiplication.Modular form 36784.2.a.w
sage: E.q_eigenform(10)