Properties

Label 279174cc
Number of curves $4$
Conductor $279174$
CM no
Rank $1$
Graph

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

Elliptic curves in class 279174cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.cc4 279174cc1 \([1, 1, 1, -173117, -45296701]\) \(-23771111713777/22848457968\) \(-551506230746199792\) \([2]\) \(4423680\) \(2.1004\) \(\Gamma_0(N)\)-optimal
279174.cc3 279174cc2 \([1, 1, 1, -3230737, -2235775669]\) \(154502321244119857/55101928644\) \(1330026604677626436\) \([2, 2]\) \(8847360\) \(2.4470\)  
279174.cc2 279174cc3 \([1, 1, 1, -3696027, -1550310441]\) \(231331938231569617/90942310746882\) \(2195126300672305809858\) \([2]\) \(17694720\) \(2.7936\)  
279174.cc1 279174cc4 \([1, 1, 1, -51687367, -143050742449]\) \(632678989847546725777/80515134\) \(1943439602469246\) \([2]\) \(17694720\) \(2.7936\)  

Rank

sage: E.rank()
 

The elliptic curves in class 279174cc have rank \(1\).

Complex multiplication

The elliptic curves in class 279174cc do not have complex multiplication.

Modular form 279174.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + 2 q^{10} - 4 q^{11} - q^{12} + 2 q^{13} + q^{14} - 2 q^{15} + q^{16} + q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.