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	3536c	Isogeny class
Conductor	3536	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	735488 = 28 · 132 · 17	Discriminant
Eigenvalues	2+  0  4 -2  2 13+ 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-23,-10]	[a1,a2,a3,a4,a6]
j	5256144/2873	j-invariant
L	2.3282144174323	L(r)(E,1)/r!
Ω	2.3282144174323	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	1768a1 14144bc1 31824i1 88400h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3536c1

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

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Quadratic twists for elliptic curve 3536c1

-4	8	-3	5	13	17
1768a1	14144bc1	31824i1	88400h1	45968e1	60112d1

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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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