Properties

Label 2496.l
Number of curves $4$
Conductor $2496$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 2496.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.l1 2496b3 \([0, -1, 0, -14977, 710497]\) \(11339065490696/351\) \(11501568\) \([2]\) \(3072\) \(0.85929\)  
2496.l2 2496b2 \([0, -1, 0, -937, 11305]\) \(22235451328/123201\) \(504631296\) \([2, 2]\) \(1536\) \(0.51272\)  
2496.l3 2496b4 \([0, -1, 0, -417, 23265]\) \(-245314376/6908733\) \(-226385362944\) \([2]\) \(3072\) \(0.85929\)  
2496.l4 2496b1 \([0, -1, 0, -92, -18]\) \(1360251712/771147\) \(49353408\) \([2]\) \(768\) \(0.16614\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2496.l have rank \(1\).

Complex multiplication

The elliptic curves in class 2496.l do not have complex multiplication.

Modular form 2496.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} + 4 q^{11} - q^{13} - 2 q^{15} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.