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	690c	Isogeny class
Conductor	690	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-3564268498800000000 = -1 · 210 · 318 · 58 · 23	Discriminant
Eigenvalues	2+ 3+ 5- -2  2 -2  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-22777,-90852059]	[a1,a2,a3,a4,a6]
j	-1306902141891515161/3564268498800000000	j-invariant
L	0.90580157455692	L(r)(E,1)/r!
Ω	0.11322519681962	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	5520be1 22080x1 2070o1 3450v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690c1

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

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Quadratic twists for elliptic curve 690c1

-4	8	-3	5	-7	-11	13	-23
5520be1	22080x1	2070o1	3450v1	33810bc1	83490br1	116610bp1	15870c1

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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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