Cremona's table of elliptic curves

72128 = 2⁶ · 7² · 23

Field	Data	Notes
Atkin-Lehner	2- 7- 23+	Signs for the Atkin-Lehner involutions
Class	72128bq	Isogeny class
Conductor	72128	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1598858056957952 = 219 · 78 · 232	Discriminant
Eigenvalues	2- -2 -2 7-  6 -4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-43969,-2996673]	[a1,a2,a3,a4,a6]
Generators	[-113:736:1]	Generators of the group modulo torsion
j	304821217/51842	j-invariant
L	3.4601150317214	L(r)(E,1)/r!
Ω	0.33351623692992	Real period
R	1.2968315513262	Regulator
r	1	Rank of the group of rational points
S	1.0000000000806	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	72128t2 18032t2 10304s2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 72128bq2

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	-2	-	6	-4	2	-4	+	10	-8	8	2	6	12	-12	6	-6	-2	-16	-2	0	-4	6	-2

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Quadratic twists for elliptic curve 72128bq2

-4	8	-7
72128t2	18032t2	10304s2

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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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