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	3536f	Isogeny class
Conductor	3536	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	13603586048 = 214 · 132 · 173	Discriminant
Eigenvalues	2-  0  2 -4  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1499,-21622]	[a1,a2,a3,a4,a6]
j	90942871473/3321188	j-invariant
L	1.5379901386322	L(r)(E,1)/r!
Ω	0.76899506931612	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	442a1 14144r1 31824bg1 88400bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3536f1

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

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Quadratic twists for elliptic curve 3536f1

-4	8	-3	5	13	17
442a1	14144r1	31824bg1	88400bp1	45968h1	60112n1

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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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