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Properties

Label 279414.cc
Number of curves $2$
Conductor $279414$
CM no
Rank $1$
Graph

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

Elliptic curves in class 279414.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279414.cc1 279414cc2 \([1, -1, 1, -194618417, -1045093827963]\) \(-23769846831649063249/3261823333284\) \(-111868951885532051935716\) \([]\) \(67568256\) \(3.4404\)  
279414.cc2 279414cc1 \([1, -1, 1, 516523, 319097517]\) \(444369620591/1540767744\) \(-52842859655056736256\) \([]\) \(9652608\) \(2.4675\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 279414.cc have rank \(1\).

Complex multiplication

The elliptic curves in class 279414.cc do not have complex multiplication.

Modular form 279414.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 5 q^{11} + 7 q^{13} + q^{14} + q^{16} - 4 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.