Properties

Label 119952.dl
Number of curves $2$
Conductor $119952$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.dl1 119952ek2 \([0, 0, 0, -846496560, 9479548208284]\) \(-1272481306550272000/5865429267\) \(-309205845521751654427392\) \([]\) \(24675840\) \(3.7107\)  
119952.dl2 119952ek1 \([0, 0, 0, -6338640, 23318771308]\) \(-534274048000/4146834123\) \(-218607248143747242517248\) \([]\) \(8225280\) \(3.1614\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 119952.dl have rank \(0\).

Complex multiplication

The elliptic curves in class 119952.dl do not have complex multiplication.

Modular form 119952.2.a.dl

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.