Cremona's table of elliptic curves

6727 = 7 · 31²

Field	Data	Notes
Atkin-Lehner	7+ 31-	Signs for the Atkin-Lehner involutions
Class	6727b	Isogeny class
Conductor	6727	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	10218313 = 73 · 313	Discriminant
Eigenvalues	1  0  2 7+ -6 -6  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-211,1224]	[a1,a2,a3,a4,a6]
j	34965783/343	j-invariant
L	1.1492472379262	L(r)(E,1)/r!
Ω	2.2984944758524	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	107632l1 60543i1 47089c1 6727a1	Quadratic twists by: -4 -3 -7 -31

Hecke Eigenvalues for elliptic curve 6727b1

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

---

Quadratic twists for elliptic curve 6727b1

-4	-3	-7	-31
107632l1	60543i1	47089c1	6727a1

---

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