Cremona's table of elliptic curves

8216 = 2³ · 13 · 79

Field	Data	Notes
Atkin-Lehner	2- 13+ 79+	Signs for the Atkin-Lehner involutions
Class	8216c	Isogeny class
Conductor	8216	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2160084992 = 211 · 132 · 792	Discriminant
Eigenvalues	2- -2 -2 -4  4 13+  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7184,-236768]	[a1,a2,a3,a4,a6]
j	20024108158754/1054729	j-invariant
L	0.51856632244451	L(r)(E,1)/r!
Ω	0.51856632244451	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16432b2 65728h2 73944h2 106808b2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8216c2

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	4	+	6	8	-8	-4	0	-4	-6	2	-4	4	6	12	-16	-4	6	+	-12	-10	2

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Quadratic twists for elliptic curve 8216c2

-4	8	-3	13
16432b2	65728h2	73944h2	106808b2

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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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