Properties

Label 3525.e
Number of curves $1$
Conductor $3525$
CM no
Rank $1$

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

Elliptic curves in class 3525.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3525.e1 3525c1 \([1, 1, 1, 162, 156]\) \(30080231/17625\) \(-275390625\) \([]\) \(1152\) \(0.30888\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3525.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3525.e do not have complex multiplication.

Modular form 3525.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{7} + 3 q^{8} + q^{9} - 2 q^{11} + q^{12} + q^{13} - 3 q^{14} - q^{16} - 3 q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display