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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 85782.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85782.s1 | 85782s1 | \([1, 0, 0, 277933, -393243903]\) | \(4746352367/136306272\) | \(-68186723632086391392\) | \([]\) | \(3654000\) | \(2.4858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 85782.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 85782.s do not have complex multiplication.Modular form 85782.2.a.s
sage: E.q_eigenform(10)