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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 435120.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.bc1 | 435120bc1 | \([0, -1, 0, 1281334, 1426192755]\) | \(51476622143744/224325674775\) | \(-1013863213426578303600\) | \([]\) | \(15434496\) | \(2.7132\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 435120.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 435120.bc do not have complex multiplication.Modular form 435120.2.a.bc
sage: E.q_eigenform(10)