Properties

Label 12696.n
Number of curves $2$
Conductor $12696$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.n1 12696l1 \([0, -1, 0, -105447, -13075920]\) \(4499456/27\) \(778097949752016\) \([2]\) \(52992\) \(1.6967\) \(\Gamma_0(N)\)-optimal
12696.n2 12696l2 \([0, -1, 0, -44612, -28114332]\) \(-21296/729\) \(-336138314292870912\) \([2]\) \(105984\) \(2.0433\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12696.n have rank \(1\).

Complex multiplication

The elliptic curves in class 12696.n do not have complex multiplication.

Modular form 12696.2.a.n

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