Properties

Label 221760ic
Number of curves $2$
Conductor $221760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ic1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760ic

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.nx2 221760ic1 [0, 0, 0, -321852, -82303846] [] 3840000 \(\Gamma_0(N)\)-optimal
221760.nx1 221760ic2 [0, 0, 0, -964452, 6892234634] [] 19200000  

Rank

sage: E.rank()
 

The elliptic curves in class 221760ic have rank \(1\).

Complex multiplication

The elliptic curves in class 221760ic do not have complex multiplication.

Modular form 221760.2.a.ic

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{7} + q^{11} + 6q^{13} + 7q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.