Properties

Label 107712x
Number of curves $2$
Conductor $107712$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 107712x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
107712.dn2 107712x1 [0, 0, 0, -6924, -179728] [2] 147456 \(\Gamma_0(N)\)-optimal
107712.dn1 107712x2 [0, 0, 0, -104844, -13066000] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 107712x have rank \(2\).

Complex multiplication

The elliptic curves in class 107712x do not have complex multiplication.

Modular form 107712.2.a.x

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.