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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 130536.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 130536.cm1 | 130536ct1 | \([0, 0, 0, 189, 34398]\) | \(54/37\) | \(-511584159744\) | \([]\) | \(178176\) | \(0.92577\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 130536.cm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 130536.cm do not have complex multiplication.Modular form 130536.2.a.cm
sage: E.q_eigenform(10)