Cremona's table of elliptic curves

690 = 2 · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 23-	Signs for the Atkin-Lehner involutions
Class	690f	Isogeny class
Conductor	690	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1904400 = 24 · 32 · 52 · 232	Discriminant
Eigenvalues	2+ 3- 5-  0  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-93,-344]	[a1,a2,a3,a4,a6]
j	87587538121/1904400	j-invariant
L	1.54139590578	L(r)(E,1)/r!
Ω	1.54139590578	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	5520r2 22080h2 2070n2 3450n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690f2

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

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Quadratic twists for elliptic curve 690f2

-4	8	-3	5	-7	-11	13	-23
5520r2	22080h2	2070n2	3450n2	33810k2	83490cr2	116610ck2	15870j2

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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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