Properties

Label 88725.f
Number of curves $1$
Conductor $88725$
CM no
Rank $2$

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

Elliptic curves in class 88725.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88725.f1 88725cp1 \([0, 1, 1, -60558, 5734694]\) \(-1375916339200/5250987\) \(-93733399816875\) \([]\) \(628992\) \(1.5399\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 88725.f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 88725.f do not have complex multiplication.

Modular form 88725.2.a.f

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