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Properties

Label 279174.cf
Number of curves $2$
Conductor $279174$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 279174.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.cf1 279174cf2 \([1, 1, 1, -7809, -1215531]\) \(-2181825073/25039686\) \(-604397148563334\) \([]\) \(1866240\) \(1.5182\)  
279174.cf2 279174cf1 \([1, 1, 1, 861, 43353]\) \(2924207/34776\) \(-839408099544\) \([]\) \(622080\) \(0.96890\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 279174.2.a.cf

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 3 q^{10} - q^{12} + 5 q^{13} - q^{14} - 3 q^{15} + q^{16} + q^{18} + 8 q^{19} + O(q^{20})\) 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.