Cremona's table of elliptic curves

522 = 2 · 3² · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 29+	Signs for the Atkin-Lehner involutions
Class	522g	Isogeny class
Conductor	522	Conductor
∏ cp	44	Product of Tamagawa factors cp
Δ	33901369344 = 211 · 39 · 292	Discriminant
Eigenvalues	2- 3+ -2  4  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-294896,-61564589]	[a1,a2,a3,a4,a6]
j	144091275020705979/1722368	j-invariant
L	2.253591182591	L(r)(E,1)/r!
Ω	0.20487192569009	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4176o2 16704j2 522b2 13050c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522g2

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

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Quadratic twists for elliptic curve 522g2

-4	8	-3	5	-7	-11	13	29
4176o2	16704j2	522b2	13050c2	25578bc2	63162l2	88218d2	15138a2

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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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