Cremona's table of elliptic curves

3570 = 2 · 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	3570x	Isogeny class
Conductor	3570	Conductor
∏ cp	2240	Product of Tamagawa factors cp
Δ	16782725759385600 = 214 · 310 · 52 · 74 · 172	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-66296,2072640]	[a1,a2,a3,a4,a6]
Generators	[-236:2260:1]	Generators of the group modulo torsion
j	32224493437735955329/16782725759385600	j-invariant
L	5.5286220467775	L(r)(E,1)/r!
Ω	0.34336281036678	Real period
R	0.11501000191255	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28560cl2 114240cn2 10710k2 17850a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570x2

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

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Quadratic twists for elliptic curve 3570x2

-4	8	-3	5	-7	17
28560cl2	114240cn2	10710k2	17850a2	24990bq2	60690bq2

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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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