Cremona's table of elliptic curves

12900 = 2² · 3 · 5² · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 43-	Signs for the Atkin-Lehner involutions
Class	12900f	Isogeny class
Conductor	12900	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1872	Modular degree for the optimal curve
Δ	-2476800 = -1 · 28 · 32 · 52 · 43	Discriminant
Eigenvalues	2- 3+ 5+ -2  1 -3  1  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,-63]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	327680/387	j-invariant
L	3.5274602005229	L(r)(E,1)/r!
Ω	1.3835649578032	Real period
R	0.42492405586359	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	51600ct1 38700k1 12900l1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12900f1

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	1	-3	1	4	-8	-2	8	8	-6	-	1	-6	5	4	-11	10	16	3	-1	4	-14

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Quadratic twists for elliptic curve 12900f1

-4	-3	5
51600ct1	38700k1	12900l1

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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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