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	6	Product of Tamagawa factors cp
Δ	6912 = 28 · 33	Discriminant
Eigenvalues	2- 3+  0 -4  0  2  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-15,22]	[a1,a2,a3,a4,a6]
j	54000	j-invariant
L	0.70109105266273	L(r)(E,1)/r!
Ω	4.2065463159764	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	144a2 576a2 36a4 900b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 36a2

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 36a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59
144a2	576a2	36a4	900b2	1764b2	4356c2	6084a2	10404b2	12996f2	19044c2	30276c2	34596d2	49284c2	60516a2	66564b2	79524a2	101124b2	125316c2

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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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