Properties

Label 86190db
Number of curves $2$
Conductor $86190$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 86190db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86190.da2 86190db1 \([1, 0, 0, 380, -79600]\) \(2761677827/1248480000\) \(-2742910560000\) \([2]\) \(202752\) \(1.0658\) \(\Gamma_0(N)\)-optimal
86190.da1 86190db2 \([1, 0, 0, -25620, -1540800]\) \(846509996114173/24354723600\) \(53507327749200\) \([2]\) \(405504\) \(1.4123\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86190db have rank \(1\).

Complex multiplication

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

Modular form 86190.2.a.db

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.