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	10296n	Isogeny class
Conductor	10296	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	21504	Modular degree for the optimal curve
Δ	9750598867152 = 24 · 318 · 112 · 13	Discriminant
Eigenvalues	2- 3- -2  4 11+ 13-  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6906,-161939]	[a1,a2,a3,a4,a6]
j	3122884507648/835956693	j-invariant
L	2.1367287544544	L(r)(E,1)/r!
Ω	0.53418218861359	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592o1 82368bs1 3432e1 113256r1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10296n1

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	4	+	-	6	0	-8	2	4	6	2	-4	0	-6	12	14	0	0	-6	0	4	-6	-6

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Quadratic twists for elliptic curve 10296n1

-4	8	-3	-11
20592o1	82368bs1	3432e1	113256r1

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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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