Properties

Label 10115l
Number of curves $1$
Conductor $10115$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 10115l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10115.j1 10115l1 \([1, 1, 0, -252, -851]\) \(6161940649/2734375\) \(790234375\) \([]\) \(5184\) \(0.40295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10115l1 has rank \(1\).

Complex multiplication

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

Modular form 10115.2.a.l

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