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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 471510o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 471510.o1 | 471510o1 | \([1, -1, 0, 554880, -5658116554]\) | \(31772115999/23274218750\) | \(-13840426031162280468750\) | \([]\) | \(39836160\) | \(2.9275\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 471510o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 471510o do not have complex multiplication.Modular form 471510.2.a.o
sage: E.q_eigenform(10)