Properties

Label 5265.f
Number of curves $1$
Conductor $5265$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 5265.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5265.f1 5265k1 \([1, -1, 1, -2, 1054]\) \(-9/8125\) \(-479773125\) \([]\) \(1728\) \(0.34462\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5265.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5265.f do not have complex multiplication.

Modular form 5265.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 3 q^{7} + 3 q^{8} - q^{10} - 5 q^{11} + q^{13} - 3 q^{14} - q^{16} + 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display