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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 69312dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69312.cr1 | 69312dk1 | \([0, 1, 0, 78939, 6131331]\) | \(70575104/61731\) | \(-47582237163700224\) | \([]\) | \(552960\) | \(1.8876\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69312dk1 has rank \(0\).
Complex multiplication
The elliptic curves in class 69312dk do not have complex multiplication.Modular form 69312.2.a.dk
sage: E.q_eigenform(10)