Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4840.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4840.f1 4840g3 \([0, 0, 0, -12947, 567006]\) \(132304644/5\) \(9070392320\) \([2]\) \(5120\) \(0.99673\)  
4840.f2 4840g2 \([0, 0, 0, -847, 7986]\) \(148176/25\) \(11337990400\) \([2, 2]\) \(2560\) \(0.65016\)  
4840.f3 4840g1 \([0, 0, 0, -242, -1331]\) \(55296/5\) \(141724880\) \([2]\) \(1280\) \(0.30359\) \(\Gamma_0(N)\)-optimal
4840.f4 4840g4 \([0, 0, 0, 1573, 45254]\) \(237276/625\) \(-1133799040000\) \([2]\) \(5120\) \(0.99673\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4840.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4q^{7} - 3q^{9} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.