Cremona's table of elliptic curves

113216 = 2⁶ · 29 · 61

Field	Data	Notes
Atkin-Lehner	2+ 29- 61-	Signs for the Atkin-Lehner involutions
Class	113216f	Isogeny class
Conductor	113216	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	22619955396608 = 219 · 294 · 61	Discriminant
Eigenvalues	2+  0  2 -4 -4  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-42764,-3396112]	[a1,a2,a3,a4,a6]
Generators	[4574:309024:1]	Generators of the group modulo torsion
j	32992767973017/86288282	j-invariant
L	4.8820071351019	L(r)(E,1)/r!
Ω	0.33204598863355	Real period
R	3.6757009861002	Regulator
r	1	Rank of the group of rational points
S	1.0000000130475	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	113216l4 3538a3	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 113216f4

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
+	0	2	-4	-4	2	6	-8	-4	-	0	6	10	-4	0	-2	-4	-	-4	12	-14	0	12	-18	-6

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Quadratic twists for elliptic curve 113216f4

-4	8
113216l4	3538a3

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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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