↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 2496.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.m1 2496e2 \([0, -1, 0, -57, 153]\) \(5088448/1053\) \(4313088\) \([2]\) \(512\) \(-0.011725\)  
2496.m2 2496e1 \([0, -1, 0, 8, 10]\) \(778688/1521\) \(-97344\) \([2]\) \(256\) \(-0.35830\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2496.2.a.m

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