Properties

Label 10115.k
Number of curves $1$
Conductor $10115$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 10115.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10115.k1 10115c1 \([1, 0, 1, -72979, -3670469]\) \(6161940649/2734375\) \(19074336752734375\) \([]\) \(88128\) \(1.8196\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10115.k1 has rank \(2\).

Complex multiplication

The elliptic curves in class 10115.k do not have complex multiplication.

Modular form 10115.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - 3 q^{8} - 2 q^{9} - q^{10} - 6 q^{11} - q^{12} - 6 q^{13} - q^{14} - q^{15} - q^{16} - 2 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display