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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 126852a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126852.b1 | 126852a1 | \([0, -1, 0, -39721, 3536302]\) | \(-507904/99\) | \(-1350979403306544\) | \([]\) | \(580320\) | \(1.6267\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 126852a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 126852a do not have complex multiplication.Modular form 126852.2.a.a
sage: E.q_eigenform(10)