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	8	Product of Tamagawa factors cp
Δ	1679616 = 28 · 38	Discriminant
Eigenvalues	2+ 3-  2  0 -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39,-70]	[a1,a2,a3,a4,a6]
j	35152/9	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	4	Number of elements in the torsion subgroup
Twists	144b2 576d2 24a1 1800s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 72a2

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 72a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
144b2	576d2	24a1	1800s2	3528l2	8712y2	12168q2	20808l2	25992bc2	38088i2	60552q2	69192l2	98568t2	121032f2

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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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