Properties

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

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Show commands: SageMath
E = EllipticCurve("dg1")
 
E.isogeny_class()
 

Elliptic curves in class 84966.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.dg1 84966dc1 \([1, 1, 1, -31211139, 68762513889]\) \(-1184052061112257/34349180544\) \(-97543458319830924852864\) \([]\) \(11612160\) \(3.1904\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84966.dg1 has rank \(1\).

Complex multiplication

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

Modular form 84966.2.a.dg

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