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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3864b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3864.a1 | 3864b1 | \([0, -1, 0, -392, -4116]\) | \(-3261064466/1917027\) | \(-3926071296\) | \([]\) | \(2400\) | \(0.54347\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3864b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 3864b do not have complex multiplication.Modular form 3864.2.a.b
sage: E.q_eigenform(10)