Cremona's table of elliptic curves

828 = 2² · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	828b	Isogeny class
Conductor	828	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	7243344 = 24 · 39 · 23	Discriminant
Eigenvalues	2- 3+ -2  2 -4 -2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-216,-1215]	[a1,a2,a3,a4,a6]
Generators	[-8:1:1]	Generators of the group modulo torsion
j	3538944/23	j-invariant
L	2.179270849647	L(r)(E,1)/r!
Ω	1.2458224987613	Real period
R	1.1661751449685	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3312j1 13248b1 828a1 20700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 828b1

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
-	+	-2	2	-4	-2	-2	-2	-	-4	0	2	0	-2	-12	2	-12	-14	2	0	6	6	-4	18	6

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Quadratic twists for elliptic curve 828b1

-4	8	-3	5	-7	-11	-23
3312j1	13248b1	828a1	20700b1	40572h1	100188k1	19044d1

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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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