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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 229320.df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.df1 | 229320cv1 | \([0, 0, 0, 14973, -64946]\) | \(10149078716/5923125\) | \(-216657866880000\) | \([]\) | \(516096\) | \(1.4402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 229320.df1 has rank \(1\).
Complex multiplication
The elliptic curves in class 229320.df do not have complex multiplication.Modular form 229320.2.a.df
sage: E.q_eigenform(10)