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	34272f	Isogeny class
Conductor	34272	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-1645056 = -1 · 29 · 33 · 7 · 17	Discriminant
Eigenvalues	2+ 3+  1 7- -5 -1 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27,82]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	-157464/119	j-invariant
L	5.9061342413584	L(r)(E,1)/r!
Ω	2.4487650213688	Real period
R	1.2059414010366	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34272x1 68544u1 34272ba1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 34272f1

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
+	+	1	-	-5	-1	-	2	4	0	2	3	-8	-11	-2	9	4	8	3	12	-9	13	-5	-7	-9

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Quadratic twists for elliptic curve 34272f1

-4	8	-3
34272x1	68544u1	34272ba1

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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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