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Properties

Label 152880ey
Number of curves $6$
Conductor $152880$
CM no
Rank $1$
Graph

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([0, -1, 0, -294016, 61419520]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, -1, 0, -294016, 61419520]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, -1, 0, -294016, 61419520]) ellisomat(E)
 

Rank

Copy content comment:Mordell-Weil rank
 
Copy content sage:E.rank()
 
Copy content gp:[lower,upper] = ellrank(E)
 
Copy content magma:Rank(E);
 

The elliptic curves in class 152880ey have rank \(1\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 152880ey do not have complex multiplication.

Modular form 152880.2.a.ey

Copy content comment:q-expansion of modular form
 
Copy content sage:E.q_eigenform(20)
 
Copy content gp:Ser(ellan(E,20),q)*q
 
Copy content magma:ModularForm(E);
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} - q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content comment:Isogeny matrix
 
Copy content sage:E.isogeny_class().matrix()
 
Copy content gp:ellisomat(E)
 

The \((i,j)\)-th 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 152880ey

Copy content comment:List of curves in the isogeny class
 
Copy content sage:E.isogeny_class().curves
 
Copy content magma:IsogenousCurves(E);
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.ch5 152880ey1 \([0, -1, 0, -294016, 61419520]\) \(5832972054001/4542720\) \(2189092721786880\) \([2]\) \(1179648\) \(1.8748\) \(\Gamma_0(N)\)-optimal
152880.ch4 152880ey2 \([0, -1, 0, -356736, 33371136]\) \(10418796526321/5038160400\) \(2427840646756761600\) \([2, 2]\) \(2359296\) \(2.2214\)  
152880.ch6 152880ey3 \([0, -1, 0, 1289664, 253330176]\) \(492271755328079/342606902820\) \(-165098944552428257280\) \([2]\) \(4718592\) \(2.5680\)  
152880.ch2 152880ey4 \([0, -1, 0, -3006656, -1982688000]\) \(6237734630203441/82168222500\) \(39596069719664640000\) \([2, 2]\) \(4718592\) \(2.5680\)  
152880.ch3 152880ey5 \([0, -1, 0, -458656, -5238012800]\) \(-22143063655441/24584858584650\) \(-11847204977153998233600\) \([2]\) \(9437184\) \(2.9145\)  
152880.ch1 152880ey6 \([0, -1, 0, -47953376, -127797546624]\) \(25306558948218234961/4478906250\) \(2158341494400000000\) \([2]\) \(9437184\) \(2.9145\)