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	12600bc	Isogeny class
Conductor	12600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2661120	Modular degree for the optimal curve
Δ	-2.2697982035136E+25	Discriminant
Eigenvalues	2+ 3- 5- 7+ -2 -3  5  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,44476125,-198765301250]	[a1,a2,a3,a4,a6]
Generators	[255337827809722012306:62270745819773624295732:4344231454155809]	Generators of the group modulo torsion
j	16683494528422270/38919722282469	j-invariant
L	4.4132493552484	L(r)(E,1)/r!
Ω	0.035049367878363	Real period
R	31.478808480686	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25200ck1 100800gq1 4200bd1 12600ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12600bc1

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	-3	5	4	5	-9	-5	10	-1	3	-12	-11	-5	9	-4	4	-6	14	-5	6	-18

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Quadratic twists for elliptic curve 12600bc1

-4	8	-3	5	-7
25200ck1	100800gq1	4200bd1	12600ca1	88200dw1

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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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