Properties

Label 47040.gp
Number of curves $8$
Conductor $47040$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47040.gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.gp1 47040dc8 \([0, 1, 0, -1101465185, 14069962595583]\) \(4791901410190533590281/41160000\) \(1269414714408960000\) \([2]\) \(10616832\) \(3.5149\)  
47040.gp2 47040dc6 \([0, 1, 0, -68843105, 219815685375]\) \(1169975873419524361/108425318400\) \(3343943017284658790400\) \([2, 2]\) \(5308416\) \(3.1684\)  
47040.gp3 47040dc7 \([0, 1, 0, -63825505, 253221862655]\) \(-932348627918877961/358766164249920\) \(-11064699901139704369643520\) \([2]\) \(10616832\) \(3.5149\)  
47040.gp4 47040dc5 \([0, 1, 0, -13665185, 19096955583]\) \(9150443179640281/184570312500\) \(5692329216000000000000\) \([2]\) \(3538944\) \(2.9656\)  
47040.gp5 47040dc3 \([0, 1, 0, -4617825, 2901224703]\) \(353108405631241/86318776320\) \(2662155607152179281920\) \([2]\) \(2654208\) \(2.8218\)  
47040.gp6 47040dc2 \([0, 1, 0, -1811105, -493097025]\) \(21302308926361/8930250000\) \(275417656786944000000\) \([2, 2]\) \(1769472\) \(2.6191\)  
47040.gp7 47040dc1 \([0, 1, 0, -1560225, -750349377]\) \(13619385906841/6048000\) \(186526243749888000\) \([2]\) \(884736\) \(2.2725\) \(\Gamma_0(N)\)-optimal
47040.gp8 47040dc4 \([0, 1, 0, 6028895, -3614985025]\) \(785793873833639/637994920500\) \(-19676388236172853248000\) \([2]\) \(3538944\) \(2.9656\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47040.gp have rank \(0\).

Complex multiplication

The elliptic curves in class 47040.gp do not have complex multiplication.

Modular form 47040.2.a.gp

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 2q^{13} + q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.