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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 320892.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 320892.z1 | 320892z1 | \([0, 1, 0, -349142361300, 79452828254889252]\) | \(-85772861682103118608759187536/59025788336118913418421\) | \(-3239091696095565353807004248806656\) | \([]\) | \(1780289280\) | \(5.3673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 320892.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 320892.z do not have complex multiplication.Modular form 320892.2.a.z
sage: E.q_eigenform(10)