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
deg	1	Modular degree for the optimal curve
Δ	-432 = -1 · 24 · 33	Discriminant
Eigenvalues	2- 3+  0 -4  0  2  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,1]	[a1,a2,a3,a4,a6]
j	0	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	144a1 576a1 36a3 900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 36a1

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 36a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59
144a1	576a1	36a3	900b1	1764b1	4356c1	6084a1	10404b1	12996f1	19044c1	30276c1	34596d1	49284c1	60516a1	66564b1	79524a1	101124b1	125316c1

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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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