Cremona's table of elliptic curves

696 = 2³ · 3 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 29+	Signs for the Atkin-Lehner involutions
Class	696b	Isogeny class
Conductor	696	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-178176 = -1 · 211 · 3 · 29	Discriminant
Eigenvalues	2+ 3- -3  1 -2  4  7  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,8,-16]	[a1,a2,a3,a4,a6]
j	24334/87	j-invariant
L	1.6317277400716	L(r)(E,1)/r!
Ω	1.6317277400716	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	1392b1 5568f1 2088l1 17400u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 696b1

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
+	-	-3	1	-2	4	7	7	0	+	4	-5	3	9	5	-6	-9	-10	4	12	-6	-10	-8	10	16

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Quadratic twists for elliptic curve 696b1

-4	8	-3	5	-7	-11	13	29
1392b1	5568f1	2088l1	17400u1	34104g1	84216u1	117624bu1	20184n1

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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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