Properties

Label 12696.s
Number of curves $2$
Conductor $12696$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12696.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.s1 12696p2 \([0, 1, 0, -63069672, -192808566720]\) \(15043017316604/243\) \(448184419057161216\) \([2]\) \(1059840\) \(2.9324\)  
12696.s2 12696p1 \([0, 1, 0, -3938052, -3019719168]\) \(-14647977776/59049\) \(-27227203457722543872\) \([2]\) \(529920\) \(2.5858\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 12696.s have rank \(0\).

Complex multiplication

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

Modular form 12696.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} + 2q^{7} + q^{9} + 4q^{11} - 6q^{13} + 2q^{15} + 6q^{17} + 6q^{19} + O(q^{20})\)  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.