Properties

Label 141960ci
Number of curves $6$
Conductor $141960$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("141960.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141960ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141960.r4 141960ci1 [0, -1, 0, -29631, 1973100] [2] 294912 \(\Gamma_0(N)\)-optimal
141960.r3 141960ci2 [0, -1, 0, -30476, 1855476] [2, 2] 589824  
141960.r5 141960ci3 [0, -1, 0, 40504, 9152220] [2] 1179648  
141960.r2 141960ci4 [0, -1, 0, -114976, -12982724] [2, 2] 1179648  
141960.r6 141960ci5 [0, -1, 0, 189224, -70294004] [2] 2359296  
141960.r1 141960ci6 [0, -1, 0, -1771176, -906668244] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 141960ci have rank \(0\).

Modular form 141960.2.a.r

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.