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	8712b	Isogeny class
Conductor	8712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	53653653504 = 211 · 39 · 113	Discriminant
Eigenvalues	2+ 3+ -2  2 11+  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12771,555390]	[a1,a2,a3,a4,a6]
Generators	[82:244:1]	Generators of the group modulo torsion
j	4293378	j-invariant
L	4.1560510088036	L(r)(E,1)/r!
Ω	1.0916342053637	Real period
R	3.8071828350402	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	17424d2 69696a2 8712o2 8712p2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712b2

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

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Quadratic twists for elliptic curve 8712b2

-4	8	-3	-11
17424d2	69696a2	8712o2	8712p2

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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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