Cremona's table of elliptic curves

570 = 2 · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 19-	Signs for the Atkin-Lehner involutions
Class	570c	Isogeny class
Conductor	570	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	10687500 = 22 · 32 · 56 · 19	Discriminant
Eigenvalues	2+ 3+ 5- -2 -2  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-397,2881]	[a1,a2,a3,a4,a6]
Generators	[-8:79:1]	Generators of the group modulo torsion
j	6947097508441/10687500	j-invariant
L	1.4027686580014	L(r)(E,1)/r!
Ω	2.2776827929964	Real period
R	0.1026458895209	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4560bb2 18240bc2 1710p2 2850y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570c2

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	-2	0	-2	-	-8	0	0	4	-8	-6	-8	-10	-8	2	0	8	-2	-8	-16	16	8

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Quadratic twists for elliptic curve 570c2

-4	8	-3	5	-7	-11	13	-19
4560bb2	18240bc2	1710p2	2850y2	27930bb2	68970bu2	96330bu2	10830be2

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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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