Properties

Label 20160c
Number of curves $2$
Conductor $20160$
CM no
Rank $1$
Graph

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

Elliptic curves in class 20160c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.l2 20160c1 \([0, 0, 0, 72, -152]\) \(1492992/1225\) \(-33868800\) \([2]\) \(4096\) \(0.13261\) \(\Gamma_0(N)\)-optimal
20160.l1 20160c2 \([0, 0, 0, -348, -1328]\) \(10536048/4375\) \(1935360000\) \([2]\) \(8192\) \(0.47919\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20160c have rank \(1\).

Complex multiplication

The elliptic curves in class 20160c do not have complex multiplication.

Modular form 20160.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 2 q^{11} + 2 q^{13} - 6 q^{17} + O(q^{20})\) 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.