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	8712f	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	25344	Modular degree for the optimal curve
Δ	-247527916810416 = -1 · 24 · 38 · 119	Discriminant
Eigenvalues	2+ 3- -2 -2 11+  0 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7986,-805255]	[a1,a2,a3,a4,a6]
j	-2048/9	j-invariant
L	0.91760837122353	L(r)(E,1)/r!
Ω	0.22940209280588	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424k1 69696bc1 2904h1 8712t1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712f1

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

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Quadratic twists for elliptic curve 8712f1

-4	8	-3	-11
17424k1	69696bc1	2904h1	8712t1

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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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