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	570i	Isogeny class
Conductor	570	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-40535043840 = -1 · 28 · 35 · 5 · 194	Discriminant
Eigenvalues	2- 3+ 5-  4  0 -6  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1900,32525]	[a1,a2,a3,a4,a6]
j	-758575480593601/40535043840	j-invariant
L	2.2660609606948	L(r)(E,1)/r!
Ω	1.1330304803474	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	4560bc1 18240bd1 1710g1 2850l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 570i1

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	-6	2	-	8	2	-8	10	6	-8	0	-2	-12	-2	-12	-8	2	-16	-4	6	-10

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Quadratic twists for elliptic curve 570i1

-4	8	-3	5	-7	-11	13	-19
4560bc1	18240bd1	1710g1	2850l1	27930cw1	68970o1	96330c1	10830p1

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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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