Properties

Label 361722.q
Number of curves $1$
Conductor $361722$
CM no
Rank $1$

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

Elliptic curves in class 361722.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361722.q1 361722q1 \([1, 1, 1, -1178131, -493393783]\) \(-3843995587427449/6390046584\) \(-300625371175320504\) \([]\) \(6967296\) \(2.2496\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 361722.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 361722.q do not have complex multiplication.

Modular form 361722.2.a.q

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