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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 209484p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.w1 | 209484p1 | \([0, 0, 0, -3143640, -79566277372]\) | \(-34801580274688000/27682340832837603\) | \(-2732914073885779470981888\) | \([]\) | \(20367360\) | \(3.3680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 209484p1 has rank \(2\).
Complex multiplication
The elliptic curves in class 209484p do not have complex multiplication.Modular form 209484.2.a.p
sage: E.q_eigenform(10)