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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 53361o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53361.cc1 | 53361o1 | \([0, 0, 1, -195657, 23853849]\) | \(1216512/343\) | \(233554159102511709\) | \([]\) | \(608256\) | \(2.0396\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53361o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 53361o do not have complex multiplication.Modular form 53361.2.a.o
sage: E.q_eigenform(10)