Properties

Label 18480.bi
Number of curves $8$
Conductor $18480$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 18480.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.bi1 18480cc7 \([0, -1, 0, -4102840, -2999791760]\) \(1864737106103260904761/129177711985836360\) \(529111908293985730560\) \([2]\) \(663552\) \(2.7244\)  
18480.bi2 18480cc4 \([0, -1, 0, -4032040, -3114928400]\) \(1769857772964702379561/691787250\) \(2833560576000\) \([2]\) \(221184\) \(2.1751\)  
18480.bi3 18480cc6 \([0, -1, 0, -810040, 224518000]\) \(14351050585434661561/3001282273281600\) \(12293252191361433600\) \([2, 2]\) \(331776\) \(2.3779\)  
18480.bi4 18480cc3 \([0, -1, 0, -763960, 257253232]\) \(12038605770121350841/757333463040\) \(3102037864611840\) \([2]\) \(165888\) \(2.0313\)  
18480.bi5 18480cc2 \([0, -1, 0, -252040, -48592400]\) \(432288716775559561/270140062500\) \(1106493696000000\) \([2, 2]\) \(110592\) \(1.8285\)  
18480.bi6 18480cc5 \([0, -1, 0, -204520, -67524368]\) \(-230979395175477481/348191894531250\) \(-1426194000000000000\) \([2]\) \(221184\) \(2.1751\)  
18480.bi7 18480cc1 \([0, -1, 0, -18760, -443408]\) \(178272935636041/81841914000\) \(335224479744000\) \([2]\) \(55296\) \(1.4820\) \(\Gamma_0(N)\)-optimal
18480.bi8 18480cc8 \([0, -1, 0, 1745480, 1353035632]\) \(143584693754978072519/276341298967965000\) \(-1131893960572784640000\) \([2]\) \(663552\) \(2.7244\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18480.bi have rank \(0\).

Complex multiplication

The elliptic curves in class 18480.bi do not have complex multiplication.

Modular form 18480.2.a.bi

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + q^{11} + 2 q^{13} - q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.