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	12600bk	Isogeny class
Conductor	12600	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	344452500000000 = 28 · 39 · 510 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7- -2  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19575,560250]	[a1,a2,a3,a4,a6]
Generators	[-95:1250:1]	Generators of the group modulo torsion
j	10536048/4375	j-invariant
L	4.6765803255388	L(r)(E,1)/r!
Ω	0.48849504033934	Real period
R	1.1966806055723	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	25200a2 100800t2 12600c2 2520a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12600bk2

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

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Quadratic twists for elliptic curve 12600bk2

-4	8	-3	5	-7
25200a2	100800t2	12600c2	2520a2	88200es2

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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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