↑

Properties

Label 194350.bi
Number of curves $1$
Conductor $194350$
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([1, -1, 0, -444505549942, 114068478199897716]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 0, -444505549942, 114068478199897716]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 0, -444505549942, 114068478199897716]) 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 194350.bi1 has rank \(0\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(5\)\(1\)
\(13\)\(1\)
\(23\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 - 7 T + 17 T^{2}\) 1.17.ah
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 194350.bi do not have complex multiplication.

Modular form 194350.2.a.bi

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);
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} + 4 q^{11} - q^{14} + q^{16} + 7 q^{17} + 3 q^{18} - 5 q^{19} + O(q^{20})\) 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 194350.bi

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
194350.bi1 194350du1 \([1, -1, 0, -444505549942, 114068478199897716]\) \(-762058709620329537263942289/2699597919027200000\) \(-34408514951533710540800000000000\) \([]\) \(1667952000\) \(5.2698\) \(\Gamma_0(N)\)-optimal