Cremona's table of elliptic curves

10224 = 2⁴ · 3² · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 71+	Signs for the Atkin-Lehner involutions
Class	10224n	Isogeny class
Conductor	10224	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	13005226377216 = 217 · 39 · 712	Discriminant
Eigenvalues	2- 3-  2 -2 -2  0  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-663339,207946330]	[a1,a2,a3,a4,a6]
Generators	[695:9090:1]	Generators of the group modulo torsion
j	10810426566289897/4355424	j-invariant
L	4.7530607211501	L(r)(E,1)/r!
Ω	0.5759563999812	Real period
R	4.1262330979439	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1278k2 40896bs2 3408h2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10224n2

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	-2	-2	0	0	4	-4	6	2	-6	0	4	0	-6	-10	0	-4	+	10	8	-8	-6	18

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Quadratic twists for elliptic curve 10224n2

-4	8	-3
1278k2	40896bs2	3408h2

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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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