Properties

Label 3600.h
Number of curves 4
Conductor 3600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3600.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3600.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.h1 3600p3 [0, 0, 0, -24075, -1437750] [2] 6144  
3600.h2 3600p2 [0, 0, 0, -1575, -20250] [2, 2] 3072  
3600.h3 3600p1 [0, 0, 0, -450, 3375] [2] 1536 \(\Gamma_0(N)\)-optimal
3600.h4 3600p4 [0, 0, 0, 2925, -114750] [2] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 3600.h have rank \(0\).

Modular form 3600.2.a.h

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.