Properties

Label 858.m
Number of curves $2$
Conductor $858$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 858.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
858.m1 858m2 \([1, 0, 0, -61, -187]\) \(25128011089/245388\) \(245388\) \([2]\) \(320\) \(-0.14637\)  
858.m2 858m1 \([1, 0, 0, -1, -7]\) \(-117649/20592\) \(-20592\) \([2]\) \(160\) \(-0.49295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 858.m have rank \(0\).

Complex multiplication

The elliptic curves in class 858.m do not have complex multiplication.

Modular form 858.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + 4 q^{10} + q^{11} + q^{12} - q^{13} - 4 q^{14} + 4 q^{15} + q^{16} + 4 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.