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Properties

Label 137280bg
Number of curves $6$
Conductor $137280$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 137280bg have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(11\)\(1 + T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(17\) \( 1 + 4 T + 17 T^{2}\) 1.17.e
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 + 8 T + 29 T^{2}\) 1.29.i
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 137280bg do not have complex multiplication.

Modular form 137280.2.a.bg

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + q^{11} - q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 137280bg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137280.ez5 137280bg1 \([0, 1, 0, -181761, -13059585]\) \(2533309721804161/1187575234560\) \(311315722288496640\) \([2]\) \(1474560\) \(2.0510\) \(\Gamma_0(N)\)-optimal
137280.ez4 137280bg2 \([0, 1, 0, -1492481, 692369919]\) \(1402524686897642881/20523074457600\) \(5380000830613094400\) \([2, 2]\) \(2949120\) \(2.3975\)  
137280.ez2 137280bg3 \([0, 1, 0, -23795201, 44668873215]\) \(5683972151443376419201/1244117160000\) \(326137848791040000\) \([2, 2]\) \(5898240\) \(2.7441\)  
137280.ez6 137280bg4 \([0, 1, 0, -161281, 1884326399]\) \(-1769848555063681/5850659851882560\) \(-1533715376211901808640\) \([2]\) \(5898240\) \(2.7441\)  
137280.ez1 137280bg5 \([0, 1, 0, -380723201, 2859188924415]\) \(23281546263261052473907201/1115400\) \(292395417600\) \([2]\) \(11796480\) \(3.0907\)  
137280.ez3 137280bg6 \([0, 1, 0, -23710721, 45001876479]\) \(-5623647484692626737921/84122230603125000\) \(-22052138019225600000000\) \([2]\) \(11796480\) \(3.0907\)