Properties

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

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

Elliptic curves in class 277350.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.cc1 277350cc2 \([1, 1, 1, -82281463, -336138727219]\) \(-337335507529/72000000\) \(-13149225312301125000000000\) \([]\) \(74898432\) \(3.5412\)  
277350.cc2 277350cc1 \([1, 1, 1, 7163912, 2680353281]\) \(222641831/145800\) \(-26627181257409778125000\) \([]\) \(24966144\) \(2.9919\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 277350.2.a.cc

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.