Cremona's table of elliptic curves

8712 = 2³ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	8712s	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1283184720745196544 = -1 · 210 · 312 · 119	Discriminant
Eigenvalues	2- 3-  2  2 11+ -4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,147741,-49925810]	[a1,a2,a3,a4,a6]
Generators	[92589:1064120:343]	Generators of the group modulo torsion
j	202612/729	j-invariant
L	5.1120300997384	L(r)(E,1)/r!
Ω	0.1383865687934	Real period
R	9.2350546449531	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424j2 69696bd2 2904e2 8712e2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712s2

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

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Quadratic twists for elliptic curve 8712s2

-4	8	-3	-11
17424j2	69696bd2	2904e2	8712e2

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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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