Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 18515q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.b1 18515q1 \([1, -1, 1, -732, 9714]\) \(-81892654209/26796875\) \(-14175546875\) \([]\) \(24192\) \(0.66035\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18515q1 has rank \(2\).

Complex multiplication

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

Modular form 18515.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} - q^{4} + q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 6 q^{9} - q^{10} - 5 q^{11} + 3 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display