Properties

Label 91035h
Number of curves 4
Conductor 91035
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("91035.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91035h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91035.bi4 91035h1 [1, -1, 0, 36360, -4497269] [2] 589824 \(\Gamma_0(N)\)-optimal
91035.bi3 91035h2 [1, -1, 0, -288765, -48909344] [2, 2] 1179648  
91035.bi2 91035h3 [1, -1, 0, -1394190, 589363051] [2] 2359296  
91035.bi1 91035h4 [1, -1, 0, -4385340, -3533456039] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 91035h have rank \(0\).

Modular form 91035.2.a.bi

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.