Cremona's table of elliptic curves

832 = 2⁶ · 13

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	832i	Isogeny class
Conductor	832	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-1703936 = -1 · 217 · 13	Discriminant
Eigenvalues	2-  1  1 -5 -2 13- -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-65,191]	[a1,a2,a3,a4,a6]
Generators	[-1:16:1]	Generators of the group modulo torsion
j	-235298/13	j-invariant
L	2.4833924059074	L(r)(E,1)/r!
Ω	2.6223391998859	Real period
R	0.23675354488995	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	832e1 208b1 7488ca1 20800cm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 832i1

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
-	1	1	-5	-2	-	-3	-2	-4	6	4	-11	8	-1	-9	12	6	0	6	-7	-2	-12	-16	-10	-10

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Quadratic twists for elliptic curve 832i1

-4	8	-3	5	-7	-11	13
832e1	208b1	7488ca1	20800cm1	40768cr1	100672cq1	10816bc1

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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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