Cremona's table of elliptic curves

57 = 3 · 19

Field	Data	Notes
Atkin-Lehner	3- 19+	Signs for the Atkin-Lehner involutions
Class	57c	Isogeny class
Conductor	57	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-22284891 = -1 · 32 · 195	Discriminant
Eigenvalues	-2 3-  1  3 -3 -6  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-4390,-113432]	[a1,a2,a3,a4,a6]
j	-9358714467168256/22284891	j-invariant
L	0.58650959165657	L(r)(E,1)/r!
Ω	0.29325479582828	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	912f2 3648f2 171c2 1425b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 57c2

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	-	1	3	-3	-6	3	+	4	-10	2	8	-8	-1	3	-6	0	7	8	12	-11	0	4	10	-2

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Quadratic twists for elliptic curve 57c2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
912f2	3648f2	171c2	1425b2	2793f2	6897g2	9633p2	16473c2	1083c2	30153i2	47937c2	54777b2	78033c2	95817e2	105393k2	125913h2

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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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