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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 55545o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55545.w1 | 55545o1 | \([0, 1, 1, -6482726, -8331358195]\) | \(-2476357085090396229632/1030161895751953125\) | \(-12533979785614013671875\) | \([]\) | \(6884352\) | \(2.9483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55545o1 has rank \(0\).
Complex multiplication
The elliptic curves in class 55545o do not have complex multiplication.Modular form 55545.2.a.o
sage: E.q_eigenform(10)