Properties

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

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

Elliptic curves in class 4560.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.c1 4560l4 \([0, -1, 0, -36956, 2745900]\) \(21804712949838544/8680921875\) \(2222316000000\) \([2]\) \(13824\) \(1.3331\)  
4560.c2 4560l3 \([0, -1, 0, -2661, 29736]\) \(130287139815424/52926616125\) \(846825858000\) \([2]\) \(6912\) \(0.98648\)  
4560.c3 4560l2 \([0, -1, 0, -1316, -13284]\) \(985329269584/252434475\) \(64623225600\) \([2]\) \(4608\) \(0.78375\)  
4560.c4 4560l1 \([0, -1, 0, -1221, -16020]\) \(12592337649664/1315845\) \(21053520\) \([2]\) \(2304\) \(0.43718\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} - 4 q^{13} + q^{15} + 6 q^{17} - q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.