Properties

Label 2496.f
Number of curves $2$
Conductor $2496$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2496.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.f1 2496r2 \([0, -1, 0, -393, 1449]\) \(1643032000/767637\) \(3144241152\) \([2]\) \(1280\) \(0.51681\)  
2496.f2 2496r1 \([0, -1, 0, -328, 2398]\) \(61162984000/41067\) \(2628288\) \([2]\) \(640\) \(0.17024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2496.f have rank \(0\).

Complex multiplication

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

Modular form 2496.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} + 4q^{11} - q^{13} - 6q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.