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SageMath
E = EllipticCurve("rc1")
E.isogeny_class()
Elliptic curves in class 176400rc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.jz1 | 176400rc1 | \([0, 0, 0, -662970, -212257465]\) | \(-46028377077760/1162261467\) | \(-813735980509057200\) | \([]\) | \(1751040\) | \(2.2208\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 176400rc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 176400rc do not have complex multiplication.Modular form 176400.2.a.rc
sage: E.q_eigenform(10)