Cremona's table of elliptic curves

252 = 2² · 3² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	252a	Isogeny class
Conductor	252	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	-4116773808 = -1 · 24 · 37 · 76	Discriminant
Eigenvalues	2- 3-  0 7-  6  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1020,12913]	[a1,a2,a3,a4,a6]
j	-10061824000/352947	j-invariant
L	1.3797968090362	L(r)(E,1)/r!
Ω	1.3797968090362	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	1008j3 4032n3 84a3 6300j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 252a3

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	-	6	2	0	-4	6	-6	8	2	-12	-4	-12	6	0	-10	8	-6	-10	-4	12	-12	-10

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Quadratic twists for elliptic curve 252a3

-4	8	-3	5	-7	-11	13	17	-19
1008j3	4032n3	84a3	6300j3	1764f3	30492n3	42588e3	72828l3	90972i3

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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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