Cremona's table of elliptic curves

72 = 2³ · 3²

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	72a	Isogeny class
Conductor	72	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	13436928 = 211 · 38	Discriminant
Eigenvalues	2+ 3-  2  0 -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3459,78302]	[a1,a2,a3,a4,a6]
j	3065617154/9	j-invariant
L	0.97326842113756	L(r)(E,1)/r!
Ω	1.9465368422751	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	144b5 576d5 24a5 1800s5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 72a5

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

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Quadratic twists for elliptic curve 72a5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
144b5	576d5	24a5	1800s5	3528l5	8712y5	12168q5	20808l5	25992bc6	38088i6	60552q6	69192l6	98568t6	121032f6

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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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