Cremona's table of elliptic curves

404 = 2² · 101

Field	Data	Notes
Atkin-Lehner	2- 101+	Signs for the Atkin-Lehner involutions
Class	404b	Isogeny class
Conductor	404	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	263757056 = 28 · 1013	Discriminant
Eigenvalues	2- -2  3  2 -6  5  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-229,-1161]	[a1,a2,a3,a4,a6]
j	5210570752/1030301	j-invariant
L	1.2437628268126	L(r)(E,1)/r!
Ω	1.2437628268126	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1616d2 6464h2 3636c2 10100c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 404b2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-2	3	2	-6	5	3	5	3	0	5	-10	12	8	-3	-6	-6	8	-10	-9	-4	5	-12	6	2

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Quadratic twists for elliptic curve 404b2

-4	8	-3	5	-7	-11	13	17	101
1616d2	6464h2	3636c2	10100c2	19796c2	48884d2	68276b2	116756a2	40804b2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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