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	1827d	Isogeny class
Conductor	1827	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1035909 = 36 · 72 · 29	Discriminant
Eigenvalues	-1 3- -2 7-  4 -2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1391,-19614]	[a1,a2,a3,a4,a6]
j	408023180713/1421	j-invariant
L	0.78179386428846	L(r)(E,1)/r!
Ω	0.78179386428846	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	29232bg2 116928cb2 203c2 45675p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1827d2

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

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Quadratic twists for elliptic curve 1827d2

-4	8	-3	5	-7	29
29232bg2	116928cb2	203c2	45675p2	12789o2	52983d2

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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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