Cremona's table of elliptic curves

22344 = 2³ · 3 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 19+	Signs for the Atkin-Lehner involutions
Class	22344s	Isogeny class
Conductor	22344	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-324550640644272 = -1 · 24 · 33 · 78 · 194	Discriminant
Eigenvalues	2+ 3-  2 7-  0  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,15713,425438]	[a1,a2,a3,a4,a6]
Generators	[37:1029:1]	Generators of the group modulo torsion
j	227910944768/172414683	j-invariant
L	7.4987559089858	L(r)(E,1)/r!
Ω	0.34703135092602	Real period
R	1.8006912749564	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	44688l1 67032cg1 3192b1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 22344s1

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	-	0	2	-2	+	-4	2	0	-10	10	4	-12	-6	4	-14	-4	-16	-10	16	-8	-6	-18

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Quadratic twists for elliptic curve 22344s1

-4	-3	-7
44688l1	67032cg1	3192b1

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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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