Cremona's table of elliptic curves

832 = 2⁶ · 13

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	832b	Isogeny class
Conductor	832	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-425984 = -1 · 215 · 13	Discriminant
Eigenvalues	2+ -1 -1  3 -2 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1,-31]	[a1,a2,a3,a4,a6]
Generators	[5:8:1]	Generators of the group modulo torsion
j	-8/13	j-invariant
L	2.0036945643805	L(r)(E,1)/r!
Ω	1.3485484416473	Real period
R	0.37145394679574	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	832a1 416a1 7488l1 20800w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 832b1

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	3	-2	+	-3	-2	4	-2	4	-5	-12	-7	-9	-4	-6	4	10	-15	-2	-8	4	2	10

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Quadratic twists for elliptic curve 832b1

-4	8	-3	5	-7	-11	13
832a1	416a1	7488l1	20800w1	40768bj1	100672bq1	10816e1

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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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