Properties

Label 246202bi
Number of curves $1$
Conductor $246202$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, 0, 0, -455409, 122583401]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 246202bi1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(11\)\(1 - T\)
\(19\)\(1\)
\(31\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - T + 3 T^{2}\) 1.3.ab
\(5\) \( 1 - 3 T + 5 T^{2}\) 1.5.ad
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 3 T + 17 T^{2}\) 1.17.d
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 4 T + 29 T^{2}\) 1.29.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 246202bi do not have complex multiplication.

Modular form 246202.2.a.bi

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} + q^{8} - 2 q^{9} + 3 q^{10} + q^{11} + q^{12} - 2 q^{13} + 2 q^{14} + 3 q^{15} + q^{16} - 3 q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 246202bi

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
246202.bi1 246202bi1 \([1, 0, 0, -455409, 122583401]\) \(-32370260203/1396736\) \(-450709524245049344\) \([]\) \(3502080\) \(2.1532\) \(\Gamma_0(N)\)-optimal