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	6195g	Isogeny class
Conductor	6195	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1561790475 = -1 · 32 · 52 · 76 · 59	Discriminant
Eigenvalues	1 3- 5- 7+ -6  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,207,1531]	[a1,a2,a3,a4,a6]
Generators	[25:137:1]	Generators of the group modulo torsion
j	987750361079/1561790475	j-invariant
L	5.7012533168499	L(r)(E,1)/r!
Ω	1.0253274034837	Real period
R	2.7802111293813	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	99120cf2 18585h2 30975f2 43365e2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6195g2

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	-	-	+	-6	2	6	4	0	-6	-2	-12	-10	10	2	6	+	-8	-6	-8	-10	-8	6	-10	-14

---

Quadratic twists for elliptic curve 6195g2

-4	-3	5	-7
99120cf2	18585h2	30975f2	43365e2

---

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