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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 21780.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21780.d1 | 21780b1 | \([0, 0, 0, -3993, -102487]\) | \(-76032/5\) | \(-463015182960\) | \([]\) | \(25344\) | \(0.99088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21780.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21780.d do not have complex multiplication.Modular form 21780.2.a.d
sage: E.q_eigenform(10)