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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 78400iz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.lk1 | 78400iz1 | \([0, 0, 0, 2450, -85750]\) | \(13824/35\) | \(-4117715000000\) | \([]\) | \(221184\) | \(1.1043\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400iz1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400iz do not have complex multiplication.Modular form 78400.2.a.iz
sage: E.q_eigenform(10)