↑

Properties

Label 143143.bj
Number of curves $1$
Conductor $143143$
CM no
Rank $1$
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, 0, 1, -102245, 12540349]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 0, 1, -102245, 12540349]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 0, 1, -102245, 12540349]) 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 143143.bj1 has rank \(1\).

L-function data

Bad L-factors:
Prime L-Factor
\(7\)\(1 - T\)
\(11\)\(1\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 - 2 T + 2 T^{2}\) 1.2.ac
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 7 T + 19 T^{2}\) 1.19.ah
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 - 8 T + 29 T^{2}\) 1.29.ai
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 143143.bj do not have complex multiplication.

Modular form 143143.2.a.bj

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);
 
\(q + 2 q^{2} + 2 q^{4} + q^{7} - 3 q^{9} + 2 q^{14} - 4 q^{16} + 2 q^{17} - 6 q^{18} + 7 q^{19} + O(q^{20})\) 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 143143.bj

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
143143.bj1 143143bj1 \([0, 0, 1, -102245, 12540349]\) \(2336256000/9317\) \(471417408018557\) \([]\) \(829440\) \(1.6724\) \(\Gamma_0(N)\)-optimal