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	3570s	Isogeny class
Conductor	3570	Conductor
∏ cp	384	Product of Tamagawa factors cp
Δ	48960807840000 = 28 · 32 · 54 · 76 · 172	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-9251,-66751]	[a1,a2,a3,a4,a6]
Generators	[-51:550:1]	Generators of the group modulo torsion
j	87557366190249649/48960807840000	j-invariant
L	4.2528332597144	L(r)(E,1)/r!
Ω	0.52287987139262	Real period
R	0.33889502257847	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	28560df2 114240eo2 10710n2 17850r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570s2

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

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Quadratic twists for elliptic curve 3570s2

-4	8	-3	5	-7	17
28560df2	114240eo2	10710n2	17850r2	24990cg2	60690cb2

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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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