Cremona's table of elliptic curves

57 = 3 · 19

Field	Data	Notes
Atkin-Lehner	3- 19+	Signs for the Atkin-Lehner involutions
Class	57b	Isogeny class
Conductor	57	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1539 = 34 · 19	Discriminant
Eigenvalues	1 3- -2  0  0  6 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-102,385]	[a1,a2,a3,a4,a6]
j	115714886617/1539	j-invariant
L	1.0853022722677	L(r)(E,1)/r!
Ω	4.3412090890707	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	912g3 3648g3 171a3 1425a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 57b3

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
1	-	-2	0	0	6	-6	+	4	2	8	-10	-2	-4	12	-6	-12	-2	-4	0	10	0	16	-2	10

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Quadratic twists for elliptic curve 57b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
912g3	3648g3	171a3	1425a3	2793c3	6897f3	9633m3	16473a3	1083b3	30153h4	47937b4	54777a4	78033b4	95817d4	105393j4	125913g4

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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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