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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 259182.df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.df1 | 259182df1 | \([1, -1, 0, -841275, 405644773]\) | \(-421375171921/210567168\) | \(-32904831088200056832\) | \([]\) | \(12570624\) | \(2.4501\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 259182.df1 has rank \(1\).
Complex multiplication
The elliptic curves in class 259182.df do not have complex multiplication.Modular form 259182.2.a.df
sage: E.q_eigenform(10)