Properties

Label 90354.m
Number of curves 4
Conductor 90354
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("90354.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.m1 90354l4 [1, 1, 1, -659946329, 4313767086311] [2] 85248000  
90354.m2 90354l2 [1, 1, 1, -262573544, -1637772491059] [2] 17049600  
90354.m3 90354l1 [1, 1, 1, -16399964, -25630950355] [2] 8524800 \(\Gamma_0(N)\)-optimal
90354.m4 90354l3 [1, 1, 1, 118083751, 461895766247] [2] 42624000  

Rank

sage: E.rank()
 

The elliptic curves in class 90354.m have rank \(1\).

Modular form 90354.2.a.m

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} - 2q^{10} - q^{11} - q^{12} - 6q^{13} - 2q^{14} + 2q^{15} + q^{16} + 2q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.