Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2496.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.r1 2496o2 \([0, 1, 0, -11609, 477447]\) \(42246001231552/14414517\) \(59041861632\) \([2]\) \(3072\) \(1.0384\)  
2496.r2 2496o1 \([0, 1, 0, -624, 9486]\) \(-420526439488/390971529\) \(-25022177856\) \([2]\) \(1536\) \(0.69180\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2496.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{5} - 2q^{7} + q^{9} - 2q^{11} + q^{13} - 2q^{15} + 6q^{17} + 2q^{19} + O(q^{20})\)  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.