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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5550r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.o1 | 5550r1 | \([1, 0, 1, -326, 2048]\) | \(9765625/888\) | \(346875000\) | \([]\) | \(2160\) | \(0.37800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5550r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5550r do not have complex multiplication.Modular form 5550.2.a.r
sage: E.q_eigenform(10)