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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 161700em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.bn1 | 161700em1 | \([0, -1, 0, -758, 20637]\) | \(-3937024/12375\) | \(-151593750000\) | \([]\) | \(165888\) | \(0.83192\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 161700em1 has rank \(1\).
Complex multiplication
The elliptic curves in class 161700em do not have complex multiplication.Modular form 161700.2.a.em
sage: E.q_eigenform(10)