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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 258570.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 258570.m1 | 258570m1 | \([1, -1, 0, -55098315, 157462633381]\) | \(-150149688795910040658889/33589356396300000\) | \(-4138242297380556300000\) | \([]\) | \(33561600\) | \(3.1407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 258570.m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 258570.m do not have complex multiplication.Modular form 258570.2.a.m
sage: E.q_eigenform(10)