Cremona's table of elliptic curves

819 = 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	819d	Isogeny class
Conductor	819	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-8653940464249899 = -1 · 314 · 77 · 133	Discriminant
Eigenvalues	-2 3- -1 7+  2 13+  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,22857,4273542]	[a1,a2,a3,a4,a6]
j	1811564780171264/11870974573731	j-invariant
L	0.59876772644105	L(r)(E,1)/r!
Ω	0.29938386322052	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	13104ca1 52416bw1 273b1 20475bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 819d1

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	-	-1	+	2	+	0	1	-3	5	9	0	-2	-1	-3	9	0	-2	10	12	15	11	-3	17	3

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Quadratic twists for elliptic curve 819d1

-4	8	-3	5	-7	-11	13
13104ca1	52416bw1	273b1	20475bb1	5733m1	99099ce1	10647g1

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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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