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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 247962w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 247962.w1 | 247962w1 | \([1, 1, 1, -5663059624, 164594969907497]\) | \(-9962948853954349032673/39910924168232832\) | \(-80460179684439968043261341568\) | \([]\) | \(487347840\) | \(4.4033\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 247962w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 247962w do not have complex multiplication.Modular form 247962.2.a.w
sage: E.q_eigenform(10)