Properties

Label 66654m
Number of curves $2$
Conductor $66654$
CM no
Rank $1$
Graph

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

Elliptic curves in class 66654m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66654.c2 66654m1 \([1, -1, 0, 14184, 2871288]\) \(2924207/34776\) \(-3752962039304856\) \([]\) \(506880\) \(1.6693\) \(\Gamma_0(N)\)-optimal
66654.c1 66654m2 \([1, -1, 0, -128646, -81027054]\) \(-2181825073/25039686\) \(-2702236917245032566\) \([]\) \(1520640\) \(2.2187\)  

Rank

sage: E.rank()
 

The elliptic curves in class 66654m have rank \(1\).

Complex multiplication

The elliptic curves in class 66654m do not have complex multiplication.

Modular form 66654.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{7} - q^{8} + 3 q^{10} + 5 q^{13} + q^{14} + q^{16} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.