Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 2496a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.h4 2496a1 \([0, -1, 0, -53, 21]\) \(16384000/9477\) \(9704448\) \([2]\) \(384\) \(0.030152\) \(\Gamma_0(N)\)-optimal
2496.h3 2496a2 \([0, -1, 0, -593, 5745]\) \(1409938000/4563\) \(74760192\) \([2]\) \(768\) \(0.37673\)  
2496.h2 2496a3 \([0, -1, 0, -2933, -60171]\) \(2725888000000/19773\) \(20247552\) \([2]\) \(1152\) \(0.57946\)  
2496.h1 2496a4 \([0, -1, 0, -2993, -57519]\) \(181037698000/14480427\) \(237247315968\) \([2]\) \(2304\) \(0.92603\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2496.2.a.a

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.