Properties

Label 374790h
Number of curves $4$
Conductor $374790$
CM no
Rank $1$
Graph

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

Elliptic curves in class 374790h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374790.h4 374790h1 \([1, 1, 0, -1261882873, -21099185282267]\) \(-250386371942892200094169/71782716130983936000\) \(-63707424798426321351868416000\) \([2]\) \(454164480\) \(4.2421\) \(\Gamma_0(N)\)-optimal
374790.h3 374790h2 \([1, 1, 0, -21415513593, -1206209255415003]\) \(1223880546761358893859301849/69832897265664000000\) \(61976953378171634909184000000\) \([2, 2]\) \(908328960\) \(4.5886\)  
374790.h2 374790h3 \([1, 1, 0, -22645593593, -1059875740407003]\) \(1447120434734326449115621849/290670009882258329856000\) \(257970703726810644340112199936000\) \([2]\) \(1816657920\) \(4.9352\)  
374790.h1 374790h4 \([1, 1, 0, -342643525113, -77199184186303707]\) \(5012808770744123733046717639129/16321500000000000\) \(14485391329441500000000000\) \([2]\) \(1816657920\) \(4.9352\)  

Rank

sage: E.rank()
 

The elliptic curves in class 374790h have rank \(1\).

Complex multiplication

The elliptic curves in class 374790h do not have complex multiplication.

Modular form 374790.2.a.h

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