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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 56784.de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.de1 | 56784cs1 | \([0, 1, 0, -1960456, -740711308]\) | \(249395415529/73513818\) | \(245626797099428978688\) | \([]\) | \(3144960\) | \(2.6183\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56784.de1 has rank \(1\).
Complex multiplication
The elliptic curves in class 56784.de do not have complex multiplication.Modular form 56784.2.a.de
sage: E.q_eigenform(10)