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	4	Product of Tamagawa factors cp
Δ	-1860960177652847607 = -1 · 312 · 7 · 298	Discriminant
Eigenvalues	1 3-  2 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,112329,-64042160]	[a1,a2,a3,a4,a6]
Generators	[296984417277290730:-11666643850166014315:203691874936472]	Generators of the group modulo torsion
j	215015459663151503/2552757445339983	j-invariant
L	3.8123863657771	L(r)(E,1)/r!
Ω	0.12959843996245	Real period
R	29.416915565355	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	29232ba5 116928ck5 609b6 45675k5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1827b6

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

---

Quadratic twists for elliptic curve 1827b6

-4	8	-3	5	-7	29
29232ba5	116928ck5	609b6	45675k5	12789f6	52983h5

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations