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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 53312.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.c1 | 53312bm1 | \([0, 0, 0, -17836, -2266544]\) | \(-1660932/4913\) | \(-1856141217824768\) | \([]\) | \(516096\) | \(1.6167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53312.c do not have complex multiplication.Modular form 53312.2.a.c
sage: E.q_eigenform(10)