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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 405600r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.r1 | 405600r1 | \([0, -1, 0, -5633, -71343663]\) | \(-1600/177957\) | \(-2198948989985280000\) | \([]\) | \(7741440\) | \(2.1984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405600r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 405600r do not have complex multiplication.Modular form 405600.2.a.r
sage: E.q_eigenform(10)