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	570a	Isogeny class
Conductor	570	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-12476160 = -1 · 28 · 33 · 5 · 192	Discriminant
Eigenvalues	2+ 3+ 5+  2 -6  0  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-98,372]	[a1,a2,a3,a4,a6]
Generators	[4:6:1]	Generators of the group modulo torsion
j	-105756712489/12476160	j-invariant
L	1.3629838037782	L(r)(E,1)/r!
Ω	2.1867251700822	Real period
R	0.62329908779845	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	4560z1 18240bp1 1710r1 2850x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570a1

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	-6	0	2	+	4	-8	-8	-4	-4	-6	-12	6	-4	2	-8	0	6	8	4	-4	12

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Quadratic twists for elliptic curve 570a1

-4	8	-3	5	-7	-11	13	-19
4560z1	18240bp1	1710r1	2850x1	27930bz1	68970bq1	96330ct1	10830bc1

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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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