Properties

Label 69366q
Number of curves $1$
Conductor $69366$
CM no
Rank $1$

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

Elliptic curves in class 69366q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69366.r1 69366q1 \([1, 1, 1, -272032, -42429247]\) \(2226300559224995953153/514813884113092608\) \(514813884113092608\) \([]\) \(828672\) \(2.1107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69366q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 69366q do not have complex multiplication.

Modular form 69366.2.a.q

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