↑

Properties

Label 113568.u
Number of curves $1$
Conductor $113568$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([0, -1, 0, -591725, -175163067]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, -1, 0, -591725, -175163067]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, -1, 0, -591725, -175163067]) 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 curve 113568.u1 has rank \(0\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(7\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - T + 5 T^{2}\) 1.5.ab
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 + T + 29 T^{2}\) 1.29.b
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 113568.u do not have complex multiplication.

Modular form 113568.2.a.u

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);
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} - 6 q^{11} - q^{15} + 6 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 113568.u

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
113568.u1 113568i1 \([0, -1, 0, -591725, -175163067]\) \(-527514112/567\) \(-24628228687835136\) \([]\) \(1517568\) \(2.0613\) \(\Gamma_0(N)\)-optimal