Properties

Label 203280.dg
Number of curves $8$
Conductor $203280$
CM no
Rank $1$
Graph

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

Elliptic curves in class 203280.dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203280.dg1 203280ck8 \([0, -1, 0, -679986160, -6824703694400]\) \(4791901410190533590281/41160000\) \(298669878312960000\) \([2]\) \(39813120\) \(3.3944\)  
203280.dg2 203280ck6 \([0, -1, 0, -42500080, -106620388928]\) \(1169975873419524361/108425318400\) \(786768140247131750400\) \([2, 2]\) \(19906560\) \(3.0478\)  
203280.dg3 203280ck7 \([0, -1, 0, -39402480, -122824554048]\) \(-932348627918877961/358766164249920\) \(-2603319888710666342891520\) \([2]\) \(39813120\) \(3.3944\)  
203280.dg4 203280ck5 \([0, -1, 0, -8436160, -9262534400]\) \(9150443179640281/184570312500\) \(1339300116000000000000\) \([2]\) \(13271040\) \(2.8451\)  
203280.dg5 203280ck3 \([0, -1, 0, -2850800, -1407059520]\) \(353108405631241/86318776320\) \(626356132643780689920\) \([2]\) \(9953280\) \(2.7012\)  
203280.dg6 203280ck2 \([0, -1, 0, -1118080, 239260672]\) \(21302308926361/8930250000\) \(64800696812544000000\) \([2, 2]\) \(6635520\) \(2.4985\)  
203280.dg7 203280ck1 \([0, -1, 0, -963200, 364032000]\) \(13619385906841/6048000\) \(43886186201088000\) \([2]\) \(3317760\) \(2.1519\) \(\Gamma_0(N)\)-optimal
203280.dg8 203280ck4 \([0, -1, 0, 3721920, 1753212672]\) \(785793873833639/637994920500\) \(-4629491381681768448000\) \([2]\) \(13271040\) \(2.8451\)  

Rank

sage: E.rank()
 

The elliptic curves in class 203280.dg have rank \(1\).

Complex multiplication

The elliptic curves in class 203280.dg do not have complex multiplication.

Modular form 203280.2.a.dg

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - 2q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.