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	690a	Isogeny class
Conductor	690	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	79350000000 = 27 · 3 · 58 · 232	Discriminant
Eigenvalues	2+ 3+ 5+ -2  6 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1748,-25392]	[a1,a2,a3,a4,a6]
Generators	[-23:69:1]	Generators of the group modulo torsion
j	591202341974089/79350000000	j-invariant
L	1.3963979049939	L(r)(E,1)/r!
Ω	0.7448541863823	Real period
R	1.874726531076	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5520bc2 22080bk2 2070s2 3450w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690a2

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	6	-2	0	-4	+	-2	-8	-4	2	-8	0	-2	-4	0	0	-8	6	-14	-6	-16	2

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Quadratic twists for elliptic curve 690a2

-4	8	-3	5	-7	-11	13	-23
5520bc2	22080bk2	2070s2	3450w2	33810bp2	83490bk2	116610ca2	15870g2

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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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