Cremona's table of elliptic curves

6200 = 2³ · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	6200k	Isogeny class
Conductor	6200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	25344	Modular degree for the optimal curve
Δ	-6054687500000000 = -1 · 28 · 517 · 31	Discriminant
Eigenvalues	2-  1 5+  0  0  2 -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-180033,-29699437]	[a1,a2,a3,a4,a6]
Generators	[2556749:20738450:4913]	Generators of the group modulo torsion
j	-161332732109824/1513671875	j-invariant
L	4.6352651454394	L(r)(E,1)/r!
Ω	0.11582126038559	Real period
R	10.005212190766	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	12400d1 49600v1 55800r1 1240a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6200k1

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	0	2	-3	1	0	6	-	-3	-11	-9	-10	1	13	8	-2	3	7	2	-9	4	-14

---

Quadratic twists for elliptic curve 6200k1

-4	8	-3	5
12400d1	49600v1	55800r1	1240a1

---

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