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	1827c	Isogeny class
Conductor	1827	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	38624607 = 38 · 7 · 292	Discriminant
Eigenvalues	-1 3-  0 7-  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-320,-2100]	[a1,a2,a3,a4,a6]
Generators	[-10:9:1]	Generators of the group modulo torsion
j	4956477625/52983	j-invariant
L	1.9407857607454	L(r)(E,1)/r!
Ω	1.1297922527246	Real period
R	0.85891267003515	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	29232y2 116928cf2 609a2 45675f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1827c2

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	-	0	-	0	-6	2	0	6	+	-4	6	10	-10	-8	-10	12	-8	12	-14	16	-14	-4	6	-8

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Quadratic twists for elliptic curve 1827c2

-4	8	-3	5	-7	29
29232y2	116928cf2	609a2	45675f2	12789g2	52983b2

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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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