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
Δ	35540674560000 = 214 · 38 · 54 · 232	Discriminant
Eigenvalues	2- 3+ 5+  0  0  6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-86411,-9808711]	[a1,a2,a3,a4,a6]
j	71356102305927901489/35540674560000	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	5520ba2 22080bi2 2070i2 3450j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690g2

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 690g2

-4	8	-3	5	-7	-11	13	-23
5520ba2	22080bi2	2070i2	3450j2	33810de2	83490d2	116610i2	15870z2

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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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