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	8712u	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	253440	Modular degree for the optimal curve
Δ	427728240248398848 = 210 · 311 · 119	Discriminant
Eigenvalues	2- 3-  4 -4 11+  6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1002243,-384911890]	[a1,a2,a3,a4,a6]
Generators	[-1328210:451170:2197]	Generators of the group modulo torsion
j	63253004/243	j-invariant
L	5.0668437198765	L(r)(E,1)/r!
Ω	0.15092342321565	Real period
R	8.3930704921735	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	17424m1 69696bh1 2904b1 8712g1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712u1

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

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Quadratic twists for elliptic curve 8712u1

-4	8	-3	-11
17424m1	69696bh1	2904b1	8712g1

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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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