Properties

Label 8325.e
Number of curves $1$
Conductor $8325$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 8325.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8325.e1 8325x1 \([0, 0, 1, -225, -844]\) \(110592/37\) \(421453125\) \([]\) \(3584\) \(0.35748\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8325.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8325.e do not have complex multiplication.

Modular form 8325.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + q^{7} + 5 q^{11} + 2 q^{13} - 2 q^{14} - 4 q^{16} + O(q^{20})\) Copy content Toggle raw display