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	22344i	Isogeny class
Conductor	22344	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-772852281264 = -1 · 24 · 32 · 710 · 19	Discriminant
Eigenvalues	2+ 3+  2 7- -4 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1993,-25500]	[a1,a2,a3,a4,a6]
Generators	[75:735:1]	Generators of the group modulo torsion
j	464857088/410571	j-invariant
L	4.5994314536166	L(r)(E,1)/r!
Ω	0.49332554243411	Real period
R	2.3308297756704	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	44688bb1 67032cs1 3192i1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 22344i1

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	-	-4	-2	-2	-	0	-2	8	-2	2	4	0	-2	12	-14	8	-12	14	-4	4	18	10

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Quadratic twists for elliptic curve 22344i1

-4	-3	-7
44688bb1	67032cs1	3192i1

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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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