Properties

Label 70560bw
Number of curves $4$
Conductor $70560$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 70560bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70560.ci3 70560bw1 \([0, 0, 0, -31017, 2068976]\) \(601211584/11025\) \(60516574977600\) \([2, 2]\) \(294912\) \(1.4393\) \(\Gamma_0(N)\)-optimal
70560.ci4 70560bw2 \([0, 0, 0, -147, 6001814]\) \(-8/354375\) \(-15561404994240000\) \([2]\) \(589824\) \(1.7858\)  
70560.ci2 70560bw3 \([0, 0, 0, -64092, -3117184]\) \(82881856/36015\) \(12651998608650240\) \([2]\) \(589824\) \(1.7858\)  
70560.ci1 70560bw4 \([0, 0, 0, -494067, 133667786]\) \(303735479048/105\) \(4610786664960\) \([2]\) \(589824\) \(1.7858\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70560bw have rank \(2\).

Complex multiplication

The elliptic curves in class 70560bw do not have complex multiplication.

Modular form 70560.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4q^{11} - 6q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.