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Properties

Label 35594.e
Number of curves $3$
Conductor $35594$
CM no
Rank $0$
Graph

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

Elliptic curves in class 35594.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35594.e1 35594d3 \([1, 0, 0, -629084, -192101104]\) \(-10730978619193/6656\) \(-17077474978304\) \([]\) \(301320\) \(1.8598\)  
35594.e2 35594d2 \([1, 0, 0, -6189, -374023]\) \(-10218313/17576\) \(-45095207364584\) \([]\) \(100440\) \(1.3105\)  
35594.e3 35594d1 \([1, 0, 0, 656, 10666]\) \(12167/26\) \(-66708886634\) \([]\) \(33480\) \(0.76123\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35594.e have rank \(0\).

Complex multiplication

The elliptic curves in class 35594.e do not have complex multiplication.

Modular form 35594.2.a.e

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.