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	6195a	Isogeny class
Conductor	6195	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	27200	Modular degree for the optimal curve
Δ	2085587888907285 = 35 · 5 · 74 · 595	Discriminant
Eigenvalues	0 3+ 5+ 7- -3 -5  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-52871,-4113703]	[a1,a2,a3,a4,a6]
Generators	[-95:206:1]	Generators of the group modulo torsion
j	16344984025413812224/2085587888907285	j-invariant
L	2.3739189946464	L(r)(E,1)/r!
Ω	0.31748714449744	Real period
R	0.37386064850029	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	99120ck1 18585m1 30975r1 43365q1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6195a1

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
0	+	+	-	-3	-5	3	7	-6	-2	-4	7	-2	5	4	-3	-	-2	11	0	7	-1	2	13	-6

---

Quadratic twists for elliptic curve 6195a1

-4	-3	5	-7
99120ck1	18585m1	30975r1	43365q1

---

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