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	816b	Isogeny class
Conductor	816	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-1539459072 = -1 · 211 · 32 · 174	Discriminant
Eigenvalues	2+ 3+  2  4 -4  6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,288,-288]	[a1,a2,a3,a4,a6]
j	1285471294/751689	j-invariant
L	1.775290563775	L(r)(E,1)/r!
Ω	0.8876452818875	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	408b4 3264be4 2448d4 20400z4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 816b4

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	4	-4	6	-	-4	4	-6	4	10	-6	-4	8	6	4	-14	12	12	10	4	-4	-6	-6

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Quadratic twists for elliptic curve 816b4

-4	8	-3	5	-7	-11	17
408b4	3264be4	2448d4	20400z4	39984r3	98736g3	13872m4

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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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