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SageMath
E = EllipticCurve("ic1")
E.isogeny_class()
Elliptic curves in class 78400ic
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.jw1 | 78400ic1 | \([0, -1, 0, -5553, -375703]\) | \(-6288640/16807\) | \(-50619564620800\) | \([]\) | \(184320\) | \(1.3171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400ic1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400ic do not have complex multiplication.Modular form 78400.2.a.ic
sage: E.q_eigenform(10)