Properties

Label 128.c
Number of curves $2$
Conductor $128$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("128.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 128.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
128.c1 128c2 [0, -1, 0, -9, -7] [2] 8  
128.c2 128c1 [0, -1, 0, 1, -1] [2] 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 128.c have rank \(0\).

Modular form 128.2.a.c

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

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 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.