Cremona's table of elliptic curves

832 = 2⁶ · 13

Field	Data	Notes
Atkin-Lehner	2+ 13-	Signs for the Atkin-Lehner involutions
Class	832f	Isogeny class
Conductor	832	Conductor
∏ cp	2	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]
j	-2146689/1664	j-invariant
L	3.0736216668361	L(r)(E,1)/r!
Ω	1.536810833418	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	832j1 26b1 7488x1 20800r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 832f1

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 832f1

-4	8	-3	5	-7	-11	13
832j1	26b1	7488x1	20800r1	40768bc1	100672y1	10816p1

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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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