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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 21175bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21175.f1 | 21175bg1 | \([1, -1, 1, 264120, -8999328]\) | \(1382658525/823543\) | \(-1213669572055758125\) | \([]\) | \(532224\) | \(2.1593\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21175bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21175bg do not have complex multiplication.Modular form 21175.2.a.bg
sage: E.q_eigenform(10)