Properties

Label 21160c
Number of curves $4$
Conductor $21160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 21160c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21160.e3 21160c1 \([0, 0, 0, -1058, -12167]\) \(55296/5\) \(11842871120\) \([2]\) \(12320\) \(0.67239\) \(\Gamma_0(N)\)-optimal
21160.e2 21160c2 \([0, 0, 0, -3703, 73002]\) \(148176/25\) \(947429689600\) \([2, 2]\) \(24640\) \(1.0190\)  
21160.e4 21160c3 \([0, 0, 0, 6877, 413678]\) \(237276/625\) \(-94742968960000\) \([2]\) \(49280\) \(1.3655\)  
21160.e1 21160c4 \([0, 0, 0, -56603, 5183142]\) \(132304644/5\) \(757943751680\) \([2]\) \(49280\) \(1.3655\)  

Rank

sage: E.rank()
 

The elliptic curves in class 21160c have rank \(0\).

Complex multiplication

The elliptic curves in class 21160c do not have complex multiplication.

Modular form 21160.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} - 3 q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.