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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5775r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5775.o1 | 5775r1 | \([0, 1, 1, -3283, 232969]\) | \(-250523582464/1369738755\) | \(-21402168046875\) | \([]\) | \(9600\) | \(1.2419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5775r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5775r do not have complex multiplication.Modular form 5775.2.a.r
sage: E.q_eigenform(10)