Properties

Label 159120.h
Number of curves $4$
Conductor $159120$
CM no
Rank $1$
Graph

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

Elliptic curves in class 159120.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.h1 159120bf3 \([0, 0, 0, -9877683, 11945968882]\) \(35694515311673154481/10400566692750\) \(31055925735484416000\) \([2]\) \(6488064\) \(2.7197\)  
159120.h2 159120bf4 \([0, 0, 0, -4834803, -3994692302]\) \(4185743240664514801/113629394531250\) \(339295554000000000000\) \([2]\) \(6488064\) \(2.7197\)  
159120.h3 159120bf2 \([0, 0, 0, -697683, 134980882]\) \(12577973014374481/4642947562500\) \(13863767134464000000\) \([2, 2]\) \(3244032\) \(2.3731\)  
159120.h4 159120bf1 \([0, 0, 0, 134637, 14960338]\) \(90391899763439/84690294000\) \(-252883862839296000\) \([2]\) \(1622016\) \(2.0265\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 159120.h have rank \(1\).

Complex multiplication

The elliptic curves in class 159120.h do not have complex multiplication.

Modular form 159120.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} + 4 q^{11} - q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.