Properties

Label 69366.a
Number of curves $1$
Conductor $69366$
CM no
Rank $2$

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

Elliptic curves in class 69366.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69366.a1 69366c1 \([1, 1, 0, -446, 2004]\) \(9845751989737/3625899552\) \(3625899552\) \([]\) \(44160\) \(0.53444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69366.a1 has rank \(2\).

Complex multiplication

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

Modular form 69366.2.a.a

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