Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 10115.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10115.a1 10115d1 \([0, 1, 1, -96, -324]\) \(1183744/245\) \(20462645\) \([]\) \(3888\) \(0.11802\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10115.a1 has rank \(2\).

Complex multiplication

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

Modular form 10115.2.a.a

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