Properties

Label 70560bs
Number of curves $4$
Conductor $70560$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 70560bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70560.ed3 70560bs1 \([0, 0, 0, -2813028897, 57426100576936]\) \(448487713888272974160064/91549016015625\) \(502515455041730025000000\) \([2, 2]\) \(41287680\) \(3.9357\) \(\Gamma_0(N)\)-optimal
70560.ed4 70560bs2 \([0, 0, 0, -2803384227, 57839426767654]\) \(-55486311952875723077768/801237030029296875\) \(-35184123938392734375000000000\) \([2]\) \(82575360\) \(4.2822\)  
70560.ed2 70560bs3 \([0, 0, 0, -2822675772, 57012396271936]\) \(7079962908642659949376/100085966990454375\) \(35160003196130573398955520000\) \([2]\) \(82575360\) \(4.2822\)  
70560.ed1 70560bs4 \([0, 0, 0, -45008460147, 3675270815038186]\) \(229625675762164624948320008/9568125\) \(420157934844480000\) \([2]\) \(82575360\) \(4.2822\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70560bs have rank \(0\).

Complex multiplication

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

Modular form 70560.2.a.bs

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.