Properties

Label 180708a
Number of curves 2
Conductor 180708
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("180708.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 180708a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
180708.m2 180708a1 [0, 1, 0, 3651, -45684] [2] 290304 \(\Gamma_0(N)\)-optimal
180708.m1 180708a2 [0, 1, 0, -16884, -407100] [2] 580608  

Rank

sage: E.rank()
 

The elliptic curves in class 180708a have rank \(0\).

Modular form 180708.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} - 2q^{7} + q^{9} + q^{11} + 2q^{13} - 2q^{15} - 4q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.