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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4025.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4025.d1 | 4025f1 | \([0, 1, 1, -8583, 303244]\) | \(-35806478336/3703\) | \(-7232421875\) | \([]\) | \(2720\) | \(0.92433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4025.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4025.d do not have complex multiplication.Modular form 4025.2.a.d
sage: E.q_eigenform(10)