Properties

Label 10080n
Number of curves $4$
Conductor $10080$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10080n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10080.b3 10080n1 \([0, 0, 0, -57408753, 167423033752]\) \(448487713888272974160064/91549016015625\) \(4271310891225000000\) \([2, 2]\) \(860160\) \(2.9627\) \(\Gamma_0(N)\)-optimal
10080.b2 10080n2 \([0, 0, 0, -57605628, 166216898752]\) \(7079962908642659949376/100085966990454375\) \(298855096058024916480000\) \([2]\) \(1720320\) \(3.3093\)  
10080.b1 10080n3 \([0, 0, 0, -918540003, 10715075262502]\) \(229625675762164624948320008/9568125\) \(3571283520000\) \([2]\) \(1720320\) \(3.3093\)  
10080.b4 10080n4 \([0, 0, 0, -57211923, 168628066378]\) \(-55486311952875723077768/801237030029296875\) \(-299060118984375000000000\) \([2]\) \(1720320\) \(3.3093\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10080n have rank \(0\).

Complex multiplication

The elliptic curves in class 10080n do not have complex multiplication.

Modular form 10080.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 4q^{11} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.