Cremona's table of elliptic curves

10680 = 2³ · 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 89-	Signs for the Atkin-Lehner involutions
Class	10680a	Isogeny class
Conductor	10680	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-200250000000000 = -1 · 210 · 32 · 512 · 89	Discriminant
Eigenvalues	2+ 3+ 5-  0 -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11880,459900]	[a1,a2,a3,a4,a6]
Generators	[365:7300:1]	Generators of the group modulo torsion
j	181065838488476/195556640625	j-invariant
L	3.8059111657114	L(r)(E,1)/r!
Ω	0.37448616496486	Real period
R	3.3876740289088	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21360e3 85440q3 32040g3 53400s3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10680a4

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	-6	-4	0	6	8	-6	10	12	-12	14	4	-2	-8	16	10	-8	-12	-	-6

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Quadratic twists for elliptic curve 10680a4

-4	8	-3	5
21360e3	85440q3	32040g3	53400s3

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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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