Properties

Label 32490.a
Number of curves $1$
Conductor $32490$
CM no
Rank $1$

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

Elliptic curves in class 32490.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.a1 32490m1 \([1, -1, 0, -27855, -1796499]\) \(-9082538350921/82944000\) \(-21828289536000\) \([]\) \(179712\) \(1.3821\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32490.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 32490.a do not have complex multiplication.

Modular form 32490.2.a.a

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