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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 69828.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69828.d1 | 69828f1 | \([0, -1, 0, -121544274, 47836559493]\) | \(299591084078848/171885556953\) | \(113929903241244133447223952\) | \([]\) | \(19593792\) | \(3.6895\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69828.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69828.d do not have complex multiplication.Modular form 69828.2.a.d
sage: E.q_eigenform(10)