Cremona's table of elliptic curves

12600 = 2³ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	12600bs	Isogeny class
Conductor	12600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	840157920000000 = 211 · 37 · 57 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-147675,-21798250]	[a1,a2,a3,a4,a6]
Generators	[-226:182:1]	Generators of the group modulo torsion
j	15267472418/36015	j-invariant
L	4.5314628256377	L(r)(E,1)/r!
Ω	0.24357593043044	Real period
R	4.6509755886283	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	25200bm4 100800cv4 4200a3 2520i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12600bs3

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	-2	2	4	0	-2	4	-2	2	-8	-4	-2	-12	-14	-8	8	2	8	-4	18	2

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Quadratic twists for elliptic curve 12600bs3

-4	8	-3	5	-7
25200bm4	100800cv4	4200a3	2520i3	88200fy4

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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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