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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 221067.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221067.bc1 | 221067bi1 | \([1, -1, 0, -31785, -3858068]\) | \(-74246873427/92019697\) | \(-4401499673799459\) | \([]\) | \(898560\) | \(1.6952\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221067.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 221067.bc do not have complex multiplication.Modular form 221067.2.a.bc
sage: E.q_eigenform(10)