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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 51714o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51714.w1 | 51714o1 | \([1, -1, 1, -2190272, -1489141533]\) | \(-1954084470169/481296384\) | \(-286211411578224377856\) | \([]\) | \(1797120\) | \(2.6435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51714o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 51714o do not have complex multiplication.Modular form 51714.2.a.o
sage: E.q_eigenform(10)