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
deg	4	Modular degree for the optimal curve
Δ	-34992 = -1 · 24 · 37	Discriminant
Eigenvalues	2+ 3-  2  0 -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,6,-7]	[a1,a2,a3,a4,a6]
j	2048/3	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	144b1 576d1 24a4 1800s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 72a1

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 72a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
144b1	576d1	24a4	1800s1	3528l1	8712y1	12168q1	20808l1	25992bc1	38088i1	60552q1	69192l1	98568t1	121032f1

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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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