↑

Properties

Label 277350cc
Number of curves $2$
Conductor $277350$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277350cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277350.cc2 277350cc1 [1, 1, 1, 7163912, 2680353281] [] 24966144 \(\Gamma_0(N)\)-optimal
277350.cc1 277350cc2 [1, 1, 1, -82281463, -336138727219] [] 74898432  

Rank

sage: E.rank()
 

The elliptic curves in class 277350cc have rank \(0\).

Complex multiplication

The elliptic curves in class 277350cc do not have complex multiplication.

Modular form 277350.2.a.cc

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - 3q^{11} - q^{12} + 4q^{13} - 2q^{14} + q^{16} + 3q^{17} + q^{18} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.