Cremona's table of elliptic curves

846 = 2 · 3² · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 47-	Signs for the Atkin-Lehner involutions
Class	846c	Isogeny class
Conductor	846	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	11799278412984 = 23 · 322 · 47	Discriminant
Eigenvalues	2+ 3- -2  0  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-19278,-1012100]	[a1,a2,a3,a4,a6]
Generators	[-75:125:1]	Generators of the group modulo torsion
j	1086913000972513/16185567096	j-invariant
L	1.6551206746339	L(r)(E,1)/r!
Ω	0.40553164387657	Real period
R	4.0813601099344	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	6768o4 27072bc3 282a4 21150bv3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 846c3

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	-2	0	0	-2	-8	-2	-2	-8	-	2	4	-10	-8	0	10	0	-12	-10	2

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Quadratic twists for elliptic curve 846c3

-4	8	-3	5	-7	-11	-47
6768o4	27072bc3	282a4	21150bv3	41454p3	102366bo3	39762j3

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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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