Properties

Label 3640.h
Number of curves $2$
Conductor $3640$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3640.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3640.h1 3640d1 \([0, -1, 0, -476, 3860]\) \(46689225424/3901625\) \(998816000\) \([2]\) \(2304\) \(0.46879\) \(\Gamma_0(N)\)-optimal
3640.h2 3640d2 \([0, -1, 0, 504, 16796]\) \(13799183324/129390625\) \(-132496000000\) \([2]\) \(4608\) \(0.81536\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3640.h have rank \(0\).

Complex multiplication

The elliptic curves in class 3640.h do not have complex multiplication.

Modular form 3640.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.