Cremona's table of elliptic curves

34272 = 2⁵ · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	34272q	Isogeny class
Conductor	34272	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	13383896399000064 = 29 · 322 · 72 · 17	Discriminant
Eigenvalues	2+ 3- -2 7-  4 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-99651,-10752730]	[a1,a2,a3,a4,a6]
Generators	[-130:70:1]	Generators of the group modulo torsion
j	293204888234504/35857918593	j-invariant
L	4.7966483377499	L(r)(E,1)/r!
Ω	0.27086069447268	Real period
R	4.4272281246718	Regulator
r	1	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34272j3 68544el3 11424q3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 34272q3

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

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Quadratic twists for elliptic curve 34272q3

-4	8	-3
34272j3	68544el3	11424q3

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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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