Cremona's table of elliptic curves

832 = 2⁶ · 13

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	832c	Isogeny class
Conductor	832	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-6815744 = -1 · 219 · 13	Discriminant
Eigenvalues	2+ -1  3 -1 -6 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,31,97]	[a1,a2,a3,a4,a6]
Generators	[9:32:1]	Generators of the group modulo torsion
j	12167/26	j-invariant
L	2.1713281808024	L(r)(E,1)/r!
Ω	1.6405548585283	Real period
R	0.33088320233775	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	832g1 26a3 7488t1 20800v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 832c1

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	3	-1	-6	+	-3	-2	0	-6	-4	7	0	1	3	0	6	-8	-14	-3	2	8	-12	-6	-10

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Quadratic twists for elliptic curve 832c1

-4	8	-3	5	-7	-11	13
832g1	26a3	7488t1	20800v1	40768bl1	100672bs1	10816i1

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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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