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	8712t	Isogeny class
Conductor	8712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-139723056 = -1 · 24 · 38 · 113	Discriminant
Eigenvalues	2- 3- -2  2 11+  0  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-66,605]	[a1,a2,a3,a4,a6]
Generators	[-2:27:1]	Generators of the group modulo torsion
j	-2048/9	j-invariant
L	4.0835346722811	L(r)(E,1)/r!
Ω	1.6012025759462	Real period
R	0.63757308625799	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	17424l1 69696bb1 2904a1 8712f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712t1

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 8712t1

-4	8	-3	-11
17424l1	69696bb1	2904a1	8712f1

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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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