Cremona's table of elliptic curves

6195 = 3 · 5 · 7 · 59

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 59-	Signs for the Atkin-Lehner involutions
Class	6195b	Isogeny class
Conductor	6195	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-12249539172885 = -1 · 3 · 5 · 712 · 59	Discriminant
Eigenvalues	-1 3+ 5+ 7-  0  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2269,-162226]	[a1,a2,a3,a4,a6]
Generators	[151:1835:1]	Generators of the group modulo torsion
j	1291859362462031/12249539172885	j-invariant
L	2.1107368899346	L(r)(E,1)/r!
Ω	0.35216535934061	Real period
R	1.9978653341399	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	99120cj3 18585n4 30975s3 43365r3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6195b4

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

---

Quadratic twists for elliptic curve 6195b4

-4	-3	5	-7
99120cj3	18585n4	30975s3	43365r3

---

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