Cremona's table of elliptic curves

11712 = 2⁶ · 3 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3- 61-	Signs for the Atkin-Lehner involutions
Class	11712o	Isogeny class
Conductor	11712	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-548683776 = -1 · 214 · 32 · 612	Discriminant
Eigenvalues	2+ 3- -2  2 -2  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,111,1071]	[a1,a2,a3,a4,a6]
Generators	[-6:15:1]	Generators of the group modulo torsion
j	9148592/33489	j-invariant
L	5.1348461940629	L(r)(E,1)/r!
Ω	1.1666518162005	Real period
R	2.20067638123	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	11712bb2 732a2 35136x2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11712o2

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

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Quadratic twists for elliptic curve 11712o2

-4	8	-3
11712bb2	732a2	35136x2

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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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