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	24	Product of Tamagawa factors cp
Δ	7792977793125 = 3 · 54 · 73 · 594	Discriminant
Eigenvalues	-1 3+ 5+ 7-  0  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7301,195998]	[a1,a2,a3,a4,a6]
Generators	[-68:653:1]	Generators of the group modulo torsion
j	43040219271568849/7792977793125	j-invariant
L	2.1107368899346	L(r)(E,1)/r!
Ω	0.70433071868123	Real period
R	0.49946633353497	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	99120cj4 18585n3 30975s4 43365r4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6195b3

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 6195b3

-4	-3	5	-7
99120cj4	18585n3	30975s4	43365r4

---

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