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	10	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-1121931 = -1 · 310 · 19	Discriminant
Eigenvalues	-2 3-  1  3 -3 -6  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,20,-32]	[a1,a2,a3,a4,a6]
j	841232384/1121931	j-invariant
L	0.58650959165657	L(r)(E,1)/r!
Ω	1.4662739791414	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	912f1 3648f1 171c1 1425b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 57c1

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 57c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
912f1	3648f1	171c1	1425b1	2793f1	6897g1	9633p1	16473c1	1083c1	30153i1	47937c1	54777b1	78033c1	95817e1	105393k1	125913h1

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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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