Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 69366e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69366.b1 69366e1 \([1, 1, 0, -82723, -10975091]\) \(-62605248418149730489/15479314352625024\) \(-15479314352625024\) \([]\) \(486864\) \(1.8246\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69366e1 has rank \(1\).

Complex multiplication

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

Modular form 69366.2.a.e

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