Properties

Label 4840.e
Number of curves $4$
Conductor $4840$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4840.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4840.e1 4840h3 \([0, 0, 0, -913187, 17284366]\) \(46424454082884/26794860125\) \(48607978698654848000\) \([2]\) \(138240\) \(2.4671\)  
4840.e2 4840h2 \([0, 0, 0, -610687, -183031134]\) \(55537159171536/228765625\) \(103749698404000000\) \([2, 2]\) \(69120\) \(2.1205\)  
4840.e3 4840h1 \([0, 0, 0, -610082, -183413131]\) \(885956203616256/15125\) \(428717762000\) \([2]\) \(34560\) \(1.7739\) \(\Gamma_0(N)\)-optimal
4840.e4 4840h4 \([0, 0, 0, -317867, -358898826]\) \(-1957960715364/29541015625\) \(-53589720250000000000\) \([2]\) \(138240\) \(2.4671\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4840.e have rank \(0\).

Complex multiplication

The elliptic curves in class 4840.e do not have complex multiplication.

Modular form 4840.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} - 3 q^{9} - 6 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.