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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 10575.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10575.c1 | 10575s1 | \([0, 0, 1, -2775, -21344]\) | \(207474688/102789\) | \(1170830953125\) | \([]\) | \(24192\) | \(1.0088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10575.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10575.c do not have complex multiplication.Modular form 10575.2.a.c
sage: E.q_eigenform(10)