Properties

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

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

Elliptic curves in class 88725.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88725.e1 88725ce1 \([0, 1, 1, -2105458, 1175290744]\) \(-647868416/63\) \(-100373116060546875\) \([]\) \(2246400\) \(2.2980\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 88725.e1 has rank \(1\).

Complex multiplication

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

Modular form 88725.2.a.e

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