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	819b	Isogeny class
Conductor	819	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-223587 = -1 · 33 · 72 · 132	Discriminant
Eigenvalues	-1 3+  0 7+  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,10,16]	[a1,a2,a3,a4,a6]
Generators	[2:5:1]	Generators of the group modulo torsion
j	4492125/8281	j-invariant
L	1.5410481141703	L(r)(E,1)/r!
Ω	2.1635462476078	Real period
R	0.35613939749941	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	13104bj2 52416m2 819a2 20475i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 819b2

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	+	0	+	0	+	2	-4	6	-4	0	-10	12	-4	-10	-12	-14	-10	0	8	2	0	-6	0	-2

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Quadratic twists for elliptic curve 819b2

-4	8	-3	5	-7	-11	13
13104bj2	52416m2	819a2	20475i2	5733b2	99099i2	10647a2

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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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