Cremona's table of elliptic curves

57222 = 2 · 3² · 11 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 17+	Signs for the Atkin-Lehner involutions
Class	57222r	Isogeny class
Conductor	57222	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-3200918507364705138 = -1 · 2 · 38 · 112 · 1710	Discriminant
Eigenvalues	2+ 3-  0 -2 11-  4 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-489042,-157157762]	[a1,a2,a3,a4,a6]
Generators	[4463:291947:1]	Generators of the group modulo torsion
j	-735091890625/181908738	j-invariant
L	4.0248108537669	L(r)(E,1)/r!
Ω	0.089106196792865	Real period
R	5.6460871950387	Regulator
r	1	Rank of the group of rational points
S	1.00000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19074m2 3366d2	Quadratic twists by: -3 17

Hecke Eigenvalues for elliptic curve 57222r2

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

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Quadratic twists for elliptic curve 57222r2

-3	17
19074m2	3366d2

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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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