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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 8085.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8085.p1 | 8085z1 | \([0, 1, 1, -415, 1306]\) | \(161702969344/75178125\) | \(3683728125\) | \([]\) | \(3360\) | \(0.53012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8085.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8085.p do not have complex multiplication.Modular form 8085.2.a.p
sage: E.q_eigenform(10)