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	64	Product of Tamagawa factors cp
Δ	128595600000000 = 210 · 38 · 58 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12675,-63250]	[a1,a2,a3,a4,a6]
Generators	[-101:432:1]	Generators of the group modulo torsion
j	19307236/11025	j-invariant
L	4.5314628256377	L(r)(E,1)/r!
Ω	0.48715186086088	Real period
R	2.3254877943142	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	25200bm2 100800cv2 4200a2 2520i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12600bs2

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 12600bs2

-4	8	-3	5	-7
25200bm2	100800cv2	4200a2	2520i2	88200fy2

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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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