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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 212415b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212415.j1 | 212415b1 | \([0, 1, 1, -4394630, -5845018966]\) | \(-1376628736/1366875\) | \(-9319717083868382716875\) | \([]\) | \(23181312\) | \(2.9113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 212415b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 212415b do not have complex multiplication.Modular form 212415.2.a.b
sage: E.q_eigenform(10)