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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 76664.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76664.d1 | 76664a1 | \([0, 0, 0, -44941532, 116236275668]\) | \(-15283295882302464/41714923579\) | \(-27399444755470617039616\) | \([]\) | \(5515776\) | \(3.1790\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76664.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 76664.d do not have complex multiplication.Modular form 76664.2.a.d
sage: E.q_eigenform(10)