Cremona's table of elliptic curves

832 = 2⁶ · 13

Field	Data	Notes
Atkin-Lehner	2- 13-	Signs for the Atkin-Lehner involutions
Class	832j	Isogeny class
Conductor	832	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-436207616 = -1 · 225 · 13	Discriminant
Eigenvalues	2- -3  1 -1 -2 13- -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-172,-1328]	[a1,a2,a3,a4,a6]
Generators	[42:256:1]	Generators of the group modulo torsion
j	-2146689/1664	j-invariant
L	1.5951492805621	L(r)(E,1)/r!
Ω	0.63783053754424	Real period
R	0.62522456462483	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	832f1 208d1 7488bz1 20800cs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 832j1

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
-	-3	1	-1	-2	-	-3	6	4	-2	-4	-3	0	-5	-13	-12	-10	8	-2	5	-10	4	0	6	14

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Quadratic twists for elliptic curve 832j1

-4	8	-3	5	-7	-11	13
832f1	208d1	7488bz1	20800cs1	40768db1	100672di1	10816bk1

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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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