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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 75712.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.dc1 | 75712ci1 | \([0, 0, 0, 35828, 4394000]\) | \(4019679/8918\) | \(-11284115006947328\) | \([]\) | \(1161216\) | \(1.7643\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.dc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712.dc do not have complex multiplication.Modular form 75712.2.a.dc
sage: E.q_eigenform(10)