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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 123840.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.gb1 | 123840gm1 | \([0, 0, 0, 69252452628, -46328599703593136]\) | \(192203697666261893287480365959/4963160303408775168000000000\) | \(-948474704346479879119699968000000000\) | \([]\) | \(1641185280\) | \(5.5835\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123840.gb1 has rank \(1\).
Complex multiplication
The elliptic curves in class 123840.gb do not have complex multiplication.Modular form 123840.2.a.gb
sage: E.q_eigenform(10)