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	3536a	Isogeny class
Conductor	3536	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	642638637056 = 211 · 13 · 176	Discriminant
Eigenvalues	2+  2  2 -2 -4 13+ 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2192,-7840]	[a1,a2,a3,a4,a6]
Generators	[88826:9359265:8]	Generators of the group modulo torsion
j	569001644066/313788397	j-invariant
L	4.8184425938544	L(r)(E,1)/r!
Ω	0.74664080414905	Real period
R	6.453494862695	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	1768b2 14144y2 31824l2 88400n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3536a2

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
+	2	2	-2	-4	+	+	-4	-4	0	-2	2	-4	4	0	-6	12	0	-12	-10	16	0	4	14	8

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Quadratic twists for elliptic curve 3536a2

-4	8	-3	5	13	17
1768b2	14144y2	31824l2	88400n2	45968a2	60112i2

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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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