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Properties

Label 86490.cg
Number of curves $2$
Conductor $86490$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 86490.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86490.cg1 86490ch2 \([1, -1, 1, -1889352608, 31609973239107]\) \(1152829477932246539641/3188367360\) \(2062842383149203824640\) \([2]\) \(31948800\) \(3.7480\)  
86490.cg2 86490ch1 \([1, -1, 1, -118037408, 494341909827]\) \(-281115640967896441/468084326400\) \(-302845964207137593753600\) \([2]\) \(15974400\) \(3.4015\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86490.cg have rank \(0\).

Complex multiplication

The elliptic curves in class 86490.cg do not have complex multiplication.

Modular form 86490.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 4 q^{7} + q^{8} - q^{10} + 2 q^{11} - 2 q^{13} + 4 q^{14} + q^{16} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.