Properties

Label 18496g
Number of curves 4
Conductor 18496
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18496.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18496g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.e4 18496g1 [0, 1, 0, -55873, 3128607] [2] 110592 \(\Gamma_0(N)\)-optimal
18496.e3 18496g2 [0, 1, 0, -795713, 272874271] [2] 221184  
18496.e2 18496g3 [0, 1, 0, -1905473, -1012893665] [2] 331776  
18496.e1 18496g4 [0, 1, 0, -2090433, -804591713] [2] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 18496g have rank \(1\).

Modular form 18496.2.a.e

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + 4q^{7} + q^{9} + 6q^{11} - 2q^{13} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.