Properties

Label 2856h
Number of curves $4$
Conductor $2856$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2856h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2856.c4 2856h1 \([0, 1, 0, -706644, 230527296]\) \(-152435594466395827792/1646846627220711\) \(-421592736568502016\) \([4]\) \(34560\) \(2.1979\) \(\Gamma_0(N)\)-optimal
2856.c3 2856h2 \([0, 1, 0, -11335464, 14685722496]\) \(157304700372188331121828/18069292138401\) \(18502955149722624\) \([2, 2]\) \(69120\) \(2.5444\)  
2856.c2 2856h3 \([0, 1, 0, -11364624, 14606337312]\) \(79260902459030376659234/842751810121431609\) \(1725955707128691935232\) \([2]\) \(138240\) \(2.8910\)  
2856.c1 2856h4 \([0, 1, 0, -181367424, 940067661600]\) \(322159999717985454060440834/4250799\) \(8705636352\) \([2]\) \(138240\) \(2.8910\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2856h have rank \(0\).

Complex multiplication

The elliptic curves in class 2856h do not have complex multiplication.

Modular form 2856.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} + q^{9} + 2 q^{13} - 2 q^{15} + q^{17} + O(q^{20})\) 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.