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	2	Product of Tamagawa factors cp
Δ	-390963 = -1 · 3 · 194	Discriminant
Eigenvalues	1 3- -2  0  0  6 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,8,29]	[a1,a2,a3,a4,a6]
j	67419143/390963	j-invariant
L	1.0853022722677	L(r)(E,1)/r!
Ω	2.1706045445353	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	912g4 3648g4 171a4 1425a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 57b4

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 57b4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
912g4	3648g4	171a4	1425a4	2793c4	6897f4	9633m4	16473a4	1083b4	30153h3	47937b3	54777a3	78033b3	95817d3	105393j3	125913g3

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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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