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	3570d	Isogeny class
Conductor	3570	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12800	Modular degree for the optimal curve
Δ	-107977095878400 = -1 · 28 · 310 · 52 · 75 · 17	Discriminant
Eigenvalues	2+ 3+ 5- 7+  0  0 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-527,499749]	[a1,a2,a3,a4,a6]
j	-16234636151161/107977095878400	j-invariant
L	0.95245989699598	L(r)(E,1)/r!
Ω	0.47622994849799	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28560dz1 114240cr1 10710y1 17850cc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3570d1

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	0	+	-6	6	-4	4	-4	-6	12	6	6	-12	-2	4	8	6	-2	-10	16	18

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Quadratic twists for elliptic curve 3570d1

-4	8	-3	5	-7	17
28560dz1	114240cr1	10710y1	17850cc1	24990z1	60690s1

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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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