Properties

Label 115920.dg
Number of curves $8$
Conductor $115920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dg1 115920dy8 \([0, 0, 0, -36561458307, -2524662991783294]\) \(1810117493172631097464564372609/125368453502655029296875000\) \(374348196263671875000000000000000\) \([2]\) \(382205952\) \(4.9982\)  
115920.dg2 115920dy6 \([0, 0, 0, -35930721027, -2621470694024446]\) \(1718043013877225552292911401729/9180538178765625000000\) \(27412940113183296000000000000\) \([2, 2]\) \(191102976\) \(4.6516\)  
115920.dg3 115920dy3 \([0, 0, 0, -35930674947, -2621477754153214]\) \(1718036403880129446396978632449/49057344000000\) \(146484444266496000000\) \([2]\) \(95551488\) \(4.3050\)  
115920.dg4 115920dy7 \([0, 0, 0, -35300721027, -2717826548024446]\) \(-1629247127728109256861881401729/125809119536174660320875000\) \(-375664017989104956923567616000000\) \([2]\) \(382205952\) \(4.9982\)  
115920.dg5 115920dy5 \([0, 0, 0, -6813644547, 215737500448514]\) \(11715873038622856702991202049/46415372499833400000000\) \(138595559638542535065600000000\) \([2]\) \(127401984\) \(4.4489\)  
115920.dg6 115920dy2 \([0, 0, 0, -632657667, -242251704574]\) \(9378698233516887309850369/5418996968417034240000\) \(16181038243741769568092160000\) \([2, 2]\) \(63700992\) \(4.1023\)  
115920.dg7 115920dy1 \([0, 0, 0, -443913987, -3590451341566]\) \(3239908336204082689644289/9880281924658790400\) \(29502363742520353593753600\) \([2]\) \(31850496\) \(3.7557\) \(\Gamma_0(N)\)-optimal
115920.dg8 115920dy4 \([0, 0, 0, 2528430333, -1937227090174]\) \(598672364899527954087397631/346996861747253448998400\) \(-1036127077227510842654038425600\) \([2]\) \(127401984\) \(4.4489\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.dg have rank \(0\).

Complex multiplication

The elliptic curves in class 115920.dg do not have complex multiplication.

Modular form 115920.2.a.dg

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.