Properties

Label 2496j
Number of curves $4$
Conductor $2496$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 2496j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.t4 2496j1 \([0, 1, 0, -1249, 354431]\) \(-822656953/207028224\) \(-54271206752256\) \([2]\) \(7680\) \(1.3147\) \(\Gamma_0(N)\)-optimal
2496.t3 2496j2 \([0, 1, 0, -83169, 9119871]\) \(242702053576633/2554695936\) \(669698211446784\) \([2, 2]\) \(15360\) \(1.6612\)  
2496.t2 2496j3 \([0, 1, 0, -149729, -7613313]\) \(1416134368422073/725251155408\) \(190120238883274752\) \([2]\) \(30720\) \(2.0078\)  
2496.t1 2496j4 \([0, 1, 0, -1327329, 588151935]\) \(986551739719628473/111045168\) \(29109824520192\) \([2]\) \(30720\) \(2.0078\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2496.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + 4 q^{7} + q^{9} + 4 q^{11} - q^{13} - 2 q^{15} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.