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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 53312c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.y1 | 53312c1 | \([0, -1, 0, -853841, 426823153]\) | \(-728871512656/410338673\) | \(-38756692663485612032\) | \([]\) | \(1806336\) | \(2.4619\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 53312c do not have complex multiplication.Modular form 53312.2.a.c
sage: E.q_eigenform(10)