Cremona's table of elliptic curves

7272 = 2³ · 3² · 101

Field	Data	Notes
Atkin-Lehner	2+ 3- 101-	Signs for the Atkin-Lehner involutions
Class	7272d	Isogeny class
Conductor	7272	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	19968	Modular degree for the optimal curve
Δ	-13844080355328 = -1 · 211 · 38 · 1013	Discriminant
Eigenvalues	2+ 3- -4  3  2 -2  1 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10947,-475810]	[a1,a2,a3,a4,a6]
Generators	[742:19998:1]	Generators of the group modulo torsion
j	-97174336898/9272709	j-invariant
L	3.500215532374	L(r)(E,1)/r!
Ω	0.23211175598621	Real period
R	2.5133119730063	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14544i1 58176t1 2424f1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7272d1

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
+	-	-4	3	2	-2	1	-1	-4	-9	2	6	0	1	12	-1	-10	7	-16	10	-2	-2	-8	0	17

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Quadratic twists for elliptic curve 7272d1

-4	8	-3
14544i1	58176t1	2424f1

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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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