Properties

Label 4560.o
Number of curves $4$
Conductor $4560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.o1 4560s4 \([0, -1, 0, -845175120, 9457603588800]\) \(16300610738133468173382620881/2228489100\) \(9127891353600\) \([2]\) \(576000\) \(3.3020\)  
4560.o2 4560s3 \([0, -1, 0, -52823440, 147788289472]\) \(-3979640234041473454886161/1471455901872240\) \(-6027083374068695040\) \([2]\) \(288000\) \(2.9554\)  
4560.o3 4560s2 \([0, -1, 0, -1407120, 553982400]\) \(75224183150104868881/11219310000000000\) \(45954293760000000000\) \([2]\) \(115200\) \(2.4973\)  
4560.o4 4560s1 \([0, -1, 0, 149360, 47192512]\) \(89962967236397039/287450726400000\) \(-1177398175334400000\) \([2]\) \(57600\) \(2.1507\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.o have rank \(0\).

Complex multiplication

The elliptic curves in class 4560.o do not have complex multiplication.

Modular form 4560.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2q^{7} + q^{9} - 2q^{11} + 4q^{13} - q^{15} - 2q^{17} + q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.