Cremona's table of elliptic curves

816 = 2⁴ · 3 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Class	816a	Isogeny class
Conductor	816	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-47941632 = -1 · 211 · 34 · 172	Discriminant
Eigenvalues	2+ 3+  0 -2  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,336]	[a1,a2,a3,a4,a6]
Generators	[2:18:1]	Generators of the group modulo torsion
j	-31250/23409	j-invariant
L	1.9819661024326	L(r)(E,1)/r!
Ω	1.6260637676611	Real period
R	0.60943677051589	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	408a2 3264w2 2448g2 20400bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 816a2

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

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Quadratic twists for elliptic curve 816a2

-4	8	-3	5	-7	-11	17
408a2	3264w2	2448g2	20400bg2	39984v2	98736n2	13872k2

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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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