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	252b	Isogeny class
Conductor	252	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-1714608 = -1 · 24 · 37 · 72	Discriminant
Eigenvalues	2- 3- -4 7+ -2 -6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12,65]	[a1,a2,a3,a4,a6]
Generators	[-2:9:1]	Generators of the group modulo torsion
j	-16384/147	j-invariant
L	1.3316363641993	L(r)(E,1)/r!
Ω	2.2699063938972	Real period
R	0.097774690018016	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	1008m1 4032j1 84b1 6300p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 252b1

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

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Quadratic twists for elliptic curve 252b1

-4	8	-3	5	-7	-11	13	17	-19
1008m1	4032j1	84b1	6300p1	1764k1	30492bm1	42588w1	72828y1	90972e1

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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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