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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 82800.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82800.z1 | 82800di1 | \([0, 0, 0, -7786875, 5313006250]\) | \(1790712239425/618098688\) | \(18023757742080000000000\) | \([]\) | \(4423680\) | \(2.9723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82800.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 82800.z do not have complex multiplication.Modular form 82800.2.a.z
sage: E.q_eigenform(10)