Properties

Label 880.h
Number of curves $4$
Conductor $880$
CM no
Rank $0$
Graph

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

Elliptic curves in class 880.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
880.h1 880i3 \([0, 0, 0, -947, -11214]\) \(22930509321/6875\) \(28160000\) \([2]\) \(256\) \(0.40748\)  
880.h2 880i4 \([0, 0, 0, -467, 3794]\) \(2749884201/73205\) \(299847680\) \([4]\) \(256\) \(0.40748\)  
880.h3 880i2 \([0, 0, 0, -67, -126]\) \(8120601/3025\) \(12390400\) \([2, 2]\) \(128\) \(0.060908\)  
880.h4 880i1 \([0, 0, 0, 13, -14]\) \(59319/55\) \(-225280\) \([2]\) \(64\) \(-0.28567\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 880.h have rank \(0\).

Complex multiplication

The elliptic curves in class 880.h do not have complex multiplication.

Modular form 880.2.a.h

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