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Properties

Label 874.f
Number of curves $2$
Conductor $874$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 874.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
874.f1 874f2 \([1, 0, 0, -640889, -197533063]\) \(29112011033527546515217/20192896\) \(20192896\) \([]\) \(4032\) \(1.6152\)  
874.f2 874f1 \([1, 0, 0, -7929, -270343]\) \(55129288688387857/484804919296\) \(484804919296\) \([3]\) \(1344\) \(1.0659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 874.f have rank \(0\).

Complex multiplication

The elliptic curves in class 874.f do not have complex multiplication.

Modular form 874.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} + q^{8} - 2 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} + 2 q^{13} + 2 q^{14} + 3 q^{15} + q^{16} - 2 q^{18} + q^{19} + O(q^{20})\) 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.