Properties

Label 10626.e
Number of curves $1$
Conductor $10626$
CM no
Rank $1$

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

Elliptic curves in class 10626.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.e1 10626h1 \([1, 0, 1, -63389, 6137528]\) \(-28167971010661685449/231722287104\) \(-231722287104\) \([]\) \(34560\) \(1.3511\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10626.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10626.e do not have complex multiplication.

Modular form 10626.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} + 5 q^{13} - q^{14} - q^{15} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display