Cremona's table of elliptic curves

1827 = 3² · 7 · 29

Field	Data	Notes
Atkin-Lehner	3- 7- 29+	Signs for the Atkin-Lehner involutions
Class	1827b	Isogeny class
Conductor	1827	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-3290588764407 = -1 · 39 · 78 · 29	Discriminant
Eigenvalues	1 3-  2 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-7056,-242501]	[a1,a2,a3,a4,a6]
Generators	[1470:55517:1]	Generators of the group modulo torsion
j	-53297461115137/4513839183	j-invariant
L	3.8123863657771	L(r)(E,1)/r!
Ω	0.2591968799249	Real period
R	3.6771144456694	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	29232ba1 116928ck1 609b1 45675k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1827b1

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
1	-	2	-	-4	-2	-2	-4	0	+	-8	-10	6	12	8	-6	-12	-10	-12	16	2	0	-4	6	-6

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Quadratic twists for elliptic curve 1827b1

-4	8	-3	5	-7	29
29232ba1	116928ck1	609b1	45675k1	12789f1	52983h1

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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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