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Properties

Label 86190g
Number of curves $4$
Conductor $86190$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 86190g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86190.l3 86190g1 \([1, 1, 0, -545873, 85325973]\) \(3726830856733921/1501644718080\) \(7248152240031006720\) \([2]\) \(3096576\) \(2.3169\) \(\Gamma_0(N)\)-optimal
86190.l2 86190g2 \([1, 1, 0, -4006993, -3028989803]\) \(1474074790091785441/32813650022400\) \(158385221250970521600\) \([2, 2]\) \(6193152\) \(2.6635\)  
86190.l4 86190g3 \([1, 1, 0, 373487, -9292200107]\) \(1193680917131039/7728836230440000\) \(-37305616276613865960000\) \([2]\) \(12386304\) \(3.0100\)  
86190.l1 86190g4 \([1, 1, 0, -63765393, -196012766763]\) \(5940441603429810927841/3044264109120\) \(14694081400277398080\) \([2]\) \(12386304\) \(3.0100\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86190g have rank \(0\).

Complex multiplication

The elliptic curves in class 86190g do not have complex multiplication.

Modular form 86190.2.a.g

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