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	690g	Isogeny class
Conductor	690	Conductor
∏ cp	112	Product of Tamagawa factors cp
deg	1792	Modular degree for the optimal curve
Δ	-12502381363200 = -1 · 228 · 34 · 52 · 23	Discriminant
Eigenvalues	2- 3+ 5+  0  0  6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4491,-207687]	[a1,a2,a3,a4,a6]
j	-10017490085065009/12502381363200	j-invariant
L	1.9492533689955	L(r)(E,1)/r!
Ω	0.27846476699936	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	5520ba1 22080bi1 2070i1 3450j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690g1

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	0	6	2	0	+	6	8	10	-6	-8	8	-6	-4	-6	8	-8	10	-8	-8	-6	18

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Quadratic twists for elliptic curve 690g1

-4	8	-3	5	-7	-11	13	-23
5520ba1	22080bi1	2070i1	3450j1	33810de1	83490d1	116610i1	15870z1

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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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