Cremona's table of elliptic curves

57 = 3 · 19

Field	Data	Notes
Atkin-Lehner	3+ 19+	Signs for the Atkin-Lehner involutions
Class	57a	Isogeny class
Conductor	57	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	-171 = -1 · 32 · 19	Discriminant
Eigenvalues	-2 3+ -3 -5  1  2 -1 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-2,2]	[a1,a2,a3,a4,a6]
Generators	[2:-2:1]	Generators of the group modulo torsion
j	-1404928/171	j-invariant
L	0.41749163967631	L(r)(E,1)/r!
Ω	5.5555045213725	Real period
R	0.037574592736824	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	912l1 3648s1 171d1 1425i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 57a1

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	+	-3	-5	1	2	-1	+	-4	-2	-6	0	0	-1	-9	10	-8	-1	8	-12	-11	16	12	-6	-10

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Quadratic twists for elliptic curve 57a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
912l1	3648s1	171d1	1425i1	2793l1	6897a1	9633d1	16473e1	1083e1	30153e1	47937f1	54777c1	78033a1	95817j1	105393w1	125913d1

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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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