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	2	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	88320 = 28 · 3 · 5 · 23	Discriminant
Eigenvalues	2+ 3- 5-  0  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13,8]	[a1,a2,a3,a4,a6]
j	217081801/88320	j-invariant
L	1.54139590578	L(r)(E,1)/r!
Ω	3.0827918115599	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	5520r1 22080h1 2070n1 3450n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690f1

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 690f1

-4	8	-3	5	-7	-11	13	-23
5520r1	22080h1	2070n1	3450n1	33810k1	83490cr1	116610ck1	15870j1

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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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