Properties

Label 4560.m
Number of curves $4$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.m1 4560r4 \([0, -1, 0, -119640, 15420912]\) \(46237740924063961/1806561830400\) \(7399677257318400\) \([2]\) \(20736\) \(1.8122\)  
4560.m2 4560r2 \([0, -1, 0, -17640, -889488]\) \(148212258825961/1218375000\) \(4990464000000\) \([2]\) \(6912\) \(1.2629\)  
4560.m3 4560r1 \([0, -1, 0, -360, -32400]\) \(-1263214441/110808000\) \(-453869568000\) \([2]\) \(3456\) \(0.91637\) \(\Gamma_0(N)\)-optimal
4560.m4 4560r3 \([0, -1, 0, 3240, 871920]\) \(918046641959/80912056320\) \(-331415782686720\) \([2]\) \(10368\) \(1.4657\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4560.m have rank \(1\).

Complex multiplication

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

Modular form 4560.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.