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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 189618bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.s1 | 189618bc1 | \([1, 0, 1, -1587928, -770389540]\) | \(-41756642210557/4634982\) | \(-49151663712866286\) | \([]\) | \(2965248\) | \(2.2316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189618bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 189618bc do not have complex multiplication.Modular form 189618.2.a.bc
sage: E.q_eigenform(10)