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SageMath
sage: E = EllipticCurve("c1")
sage: E.isogeny_class()
Elliptic curves in class 575.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
575.c1 | 575d1 | \([1, -1, 1, -55, 72]\) | \(46305/23\) | \(8984375\) | \([]\) | \(60\) | \(0.027223\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 575.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 575.c do not have complex multiplication.Modular form 575.2.a.c
sage: E.q_eigenform(10)