Properties

Label 84966.dq
Number of curves $1$
Conductor $84966$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 84966.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.dq1 84966ee1 \([1, 0, 0, 25673598, -21395871036]\) \(2280364702703/1560674304\) \(-1280831179142872506433536\) \([]\) \(19975680\) \(3.3144\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84966.dq1 has rank \(1\).

Complex multiplication

The elliptic curves in class 84966.dq do not have complex multiplication.

Modular form 84966.2.a.dq

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