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	11712s	Isogeny class
Conductor	11712	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	971440128 = 216 · 35 · 61	Discriminant
Eigenvalues	2- 3+  2  0  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1264897,-547137503]	[a1,a2,a3,a4,a6]
j	3415148655243588868/14823	j-invariant
L	2.5624667602773	L(r)(E,1)/r!
Ω	0.14235926445985	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	36	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11712j4 2928e3 35136bw4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11712s3

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

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Quadratic twists for elliptic curve 11712s3

-4	8	-3
11712j4	2928e3	35136bw4

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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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