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Properties

Label 71058.m
Number of curves $2$
Conductor $71058$
CM no
Rank $1$
Graph

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

Elliptic curves in class 71058.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71058.m1 71058l2 \([1, 0, 0, -307716981, -2077644355683]\) \(3222389999241959100048447349969/81236880320586561709476\) \(81236880320586561709476\) \([]\) \(16134720\) \(3.5040\)  
71058.m2 71058l1 \([1, 0, 0, -5118321, 4456008297]\) \(14828809162780998661814929/2048285853033578496\) \(2048285853033578496\) \([7]\) \(2304960\) \(2.5311\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 71058.m have rank \(1\).

Complex multiplication

The elliptic curves in class 71058.m do not have complex multiplication.

Modular form 71058.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.