Cremona's table of elliptic curves

3536 = 2⁴ · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	3536j	Isogeny class
Conductor	3536	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	20564436385792 = 216 · 13 · 176	Discriminant
Eigenvalues	2-  0 -4  2  2 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19387,-1015830]	[a1,a2,a3,a4,a6]
Generators	[-73:102:1]	Generators of the group modulo torsion
j	196741326427281/5020614352	j-invariant
L	2.8214850028165	L(r)(E,1)/r!
Ω	0.40522653319655	Real period
R	1.1604558486335	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	442b2 14144ba2 31824y2 88400bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3536j2

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	-4	2	2	+	-	0	4	2	2	0	0	-4	8	-6	-8	-2	-16	14	-16	-8	12	-18	-4

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Quadratic twists for elliptic curve 3536j2

-4	8	-3	5	13	17
442b2	14144ba2	31824y2	88400bg2	45968q2	60112o2

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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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