↑

Properties

Label 264264.bp
Number of curves $1$
Conductor $264264$
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, 1, 0, 2743, -67509]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 1, 0, 2743, -67509]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 1, 0, 2743, -67509]) 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 264264.bp1 has rank \(1\).

L-function data

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

Complex multiplication

The elliptic curves in class 264264.bp do not have complex multiplication.

Modular form 264264.2.a.bp

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);
 
\(q + q^{3} - 3 q^{5} - q^{7} + q^{9} + q^{13} - 3 q^{15} - 7 q^{19} + O(q^{20})\) 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 264264.bp

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
264264.bp1 264264bp1 \([0, 1, 0, 2743, -67509]\) \(5030912/7371\) \(-3342893089536\) \([]\) \(537600\) \(1.0886\) \(\Gamma_0(N)\)-optimal