Properties

Label 18515.e
Number of curves $1$
Conductor $18515$
CM no
Rank $2$

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

Elliptic curves in class 18515.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.e1 18515b1 \([1, 1, 1, -11, -156]\) \(-529/35\) \(-9794435\) \([]\) \(3840\) \(0.021213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18515.e1 has rank \(2\).

Complex multiplication

The elliptic curves in class 18515.e do not have complex multiplication.

Modular form 18515.2.a.e

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