Properties

Label 86640dd
Number of curves $2$
Conductor $86640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dd1")
 
E.isogeny_class()
 

Elliptic curves in class 86640dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.db2 86640dd1 \([0, 1, 0, -13651696, -988203820]\) \(212883113611/122880000\) \(162414036185430097920000\) \([2]\) \(14008320\) \(3.1432\) \(\Gamma_0(N)\)-optimal
86640.db1 86640dd2 \([0, 1, 0, -154124016, -734647036716]\) \(306331959547531/900000000\) \(1189555929092505600000000\) \([2]\) \(28016640\) \(3.4898\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86640dd have rank \(1\).

Complex multiplication

The elliptic curves in class 86640dd do not have complex multiplication.

Modular form 86640.2.a.dd

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4 q^{7} + q^{9} - 6 q^{11} + 4 q^{13} - q^{15} + 6 q^{17} + O(q^{20})\) 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.