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	570d	Isogeny class
Conductor	570	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	3152005008998400 = 214 · 310 · 52 · 194	Discriminant
Eigenvalues	2+ 3- 5+  4  0  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-78244,-7985758]	[a1,a2,a3,a4,a6]
j	52974743974734147769/3152005008998400	j-invariant
L	1.4325831504345	L(r)(E,1)/r!
Ω	0.28651663008689	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4560q2 18240x2 1710s2 2850q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570d2

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
+	-	+	4	0	2	-2	+	0	10	0	2	2	-4	0	-6	8	6	12	0	-14	0	-12	10	2

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Quadratic twists for elliptic curve 570d2

-4	8	-3	5	-7	-11	13	-19
4560q2	18240x2	1710s2	2850q2	27930t2	68970cq2	96330di2	10830u2

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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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