Properties

Label 2496.p
Number of curves $2$
Conductor $2496$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2496.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.p1 2496p1 \([0, 1, 0, -2605, 47219]\) \(1909913257984/129730653\) \(132844188672\) \([2]\) \(3840\) \(0.88296\) \(\Gamma_0(N)\)-optimal
2496.p2 2496p2 \([0, 1, 0, 2255, 207599]\) \(77366117936/1172914587\) \(-19217032593408\) \([2]\) \(7680\) \(1.2295\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2496.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.