Cremona's table of elliptic curves

36 = 2² · 3²

Field	Data	Notes
Atkin-Lehner	2- 3+	Signs for the Atkin-Lehner involutions
Class	36a	Isogeny class
Conductor	36	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-314928 = -1 · 24 · 39	Discriminant
Eigenvalues	2- 3+  0 -4  0  2  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-27]	[a1,a2,a3,a4,a6]
j	0	j-invariant
L	0.70109105266273	L(r)(E,1)/r!
Ω	1.4021821053255	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	144a3 576a3 36a1 900b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 36a3

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	0	2	0	8	0	0	-4	-10	0	8	0	0	0	14	-16	0	-10	-4	0	0	14

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Quadratic twists for elliptic curve 36a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59
144a3	576a3	36a1	900b3	1764b3	4356c3	6084a3	10404b3	12996f3	19044c3	30276c3	34596d3	49284c3	60516a3	66564b3	79524a3	101124b3	125316c3

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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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