Properties

Label 47096.h
Number of curves $4$
Conductor $47096$
CM no
Rank $0$
Graph

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

Elliptic curves in class 47096.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.h1 47096d4 \([0, 0, 0, -3642371, -2675619634]\) \(8773811642628/203\) \(123647113382912\) \([2]\) \(591360\) \(2.2268\)  
47096.h2 47096d2 \([0, 0, 0, -227911, -41705190]\) \(8597884752/41209\) \(6275091004182784\) \([2, 2]\) \(295680\) \(1.8802\)  
47096.h3 47096d3 \([0, 0, 0, -110171, -84727386]\) \(-242793828/4950967\) \(-3015629448295840768\) \([2]\) \(591360\) \(2.2268\)  
47096.h4 47096d1 \([0, 0, 0, -21866, 121945]\) \(121485312/69629\) \(662671248286544\) \([4]\) \(147840\) \(1.5336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47096.h have rank \(0\).

Complex multiplication

The elliptic curves in class 47096.h do not have complex multiplication.

Modular form 47096.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.