Properties

Label 12936j
Number of curves $4$
Conductor $12936$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 12936j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12936.t3 12936j1 \([0, 1, 0, -604, 5312]\) \(810448/33\) \(993898752\) \([2]\) \(6144\) \(0.49222\) \(\Gamma_0(N)\)-optimal
12936.t2 12936j2 \([0, 1, 0, -1584, -17424]\) \(3650692/1089\) \(131194635264\) \([2, 2]\) \(12288\) \(0.83879\)  
12936.t1 12936j3 \([0, 1, 0, -23144, -1362768]\) \(5690357426/891\) \(214682130432\) \([2]\) \(24576\) \(1.1854\)  
12936.t4 12936j4 \([0, 1, 0, 4296, -111504]\) \(36382894/43923\) \(-10583033911296\) \([2]\) \(24576\) \(1.1854\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12936j have rank \(0\).

Complex multiplication

The elliptic curves in class 12936j do not have complex multiplication.

Modular form 12936.2.a.j

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