Cremona's table of elliptic curves

12810 = 2 · 3 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+ 61+	Signs for the Atkin-Lehner involutions
Class	12810s	Isogeny class
Conductor	12810	Conductor
∏ cp	1152	Product of Tamagawa factors cp
Δ	4899883290624000000 = 218 · 38 · 56 · 72 · 612	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1308031,-565978855]	[a1,a2,a3,a4,a6]
Generators	[-682:3341:1]	Generators of the group modulo torsion
j	247501504481446827885169/4899883290624000000	j-invariant
L	7.5867304904799	L(r)(E,1)/r!
Ω	0.14134078756123	Real period
R	0.74551202544116	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	102480bd2 38430r2 64050g2 89670bt2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12810s2

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
-	-	+	+	-4	2	2	0	0	-6	-8	6	2	4	0	-10	-4	+	-4	12	-10	-12	4	14	-18

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Quadratic twists for elliptic curve 12810s2

-4	-3	5	-7
102480bd2	38430r2	64050g2	89670bt2

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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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