Cremona's table of elliptic curves

107712 = 2⁶ · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 17-	Signs for the Atkin-Lehner involutions
Class	107712fa	Isogeny class
Conductor	107712	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1185112540643328 = 216 · 39 · 11 · 174	Discriminant
Eigenvalues	2- 3-  2 -4 11-  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-231564,42857872]	[a1,a2,a3,a4,a6]
Generators	[-294:9248:1]	Generators of the group modulo torsion
j	28742820444292/24805737	j-invariant
L	7.3419252628438	L(r)(E,1)/r!
Ω	0.48364610581777	Real period
R	1.8975458369434	Regulator
r	1	Rank of the group of rational points
S	1.0000000034945	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107712bm4 26928p4 35904cm4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 107712fa4

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

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Quadratic twists for elliptic curve 107712fa4

-4	8	-3
107712bm4	26928p4	35904cm4

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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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