Properties

Label 121c
Number of curves 2
Conductor 121
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("121.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 121c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121.c2 121c1 [1, 1, 0, -2, -7] [] 6 \(\Gamma_0(N)\)-optimal
121.c1 121c2 [1, 1, 0, -3632, 82757] [] 66  

Rank

sage: E.rank()
 

The elliptic curves in class 121c have rank \(0\).

Modular form 121.2.a.c

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} - q^{4} + q^{5} + 2q^{6} - 2q^{7} - 3q^{8} + q^{9} + q^{10} - 2q^{12} + q^{13} - 2q^{14} + 2q^{15} - q^{16} - 5q^{17} + q^{18} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.