Cremona's table of elliptic curves

10296 = 2³ · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	10296h	Isogeny class
Conductor	10296	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	69654636260352 = 210 · 39 · 112 · 134	Discriminant
Eigenvalues	2- 3+ -4 -2 11- 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-17307,778950]	[a1,a2,a3,a4,a6]
Generators	[19:676:1]	Generators of the group modulo torsion
j	28444469868/3455881	j-invariant
L	2.8157877244526	L(r)(E,1)/r!
Ω	0.59544269357133	Real period
R	1.1822244839231	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	20592a2 82368h2 10296a2 113256h2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10296h2

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

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Quadratic twists for elliptic curve 10296h2

-4	8	-3	-11
20592a2	82368h2	10296a2	113256h2

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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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