Properties

Label 43758h
Number of curves $4$
Conductor $43758$
CM no
Rank $0$
Graph

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

Elliptic curves in class 43758h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.i4 43758h1 \([1, -1, 0, 8058024, 966722366272]\) \(79374649975090937760383/553856914190911653543936\) \(-403761690445174595433529344\) \([2]\) \(18911232\) \(3.7842\) \(\Gamma_0(N)\)-optimal
43758.i3 43758h2 \([1, -1, 0, -1419316056, 20183459605312]\) \(433744050935826360922067531137/9612122270219882316693504\) \(7007237134990294208869564416\) \([2, 2]\) \(37822464\) \(4.1307\)  
43758.i2 43758h3 \([1, -1, 0, -3089739096, -36353344521920]\) \(4474676144192042711273397261697/1806328356954994499451382272\) \(1316813372220190990100057676288\) \([2]\) \(75644928\) \(4.4773\)  
43758.i1 43758h4 \([1, -1, 0, -22586878296, 1306574318542144]\) \(1748094148784980747354970849498497/887694600425282263291392\) \(647129363710030769939424768\) \([2]\) \(75644928\) \(4.4773\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43758h have rank \(0\).

Complex multiplication

The elliptic curves in class 43758h do not have complex multiplication.

Modular form 43758.2.a.h

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