Cremona's table of elliptic curves

12200 = 2³ · 5² · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 61+	Signs for the Atkin-Lehner involutions
Class	12200k	Isogeny class
Conductor	12200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	1952000 = 28 · 53 · 61	Discriminant
Eigenvalues	2-  0 5-  0  6 -4  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-95,-350]	[a1,a2,a3,a4,a6]
Generators	[-6:2:1]	Generators of the group modulo torsion
j	2963088/61	j-invariant
L	4.6782398217892	L(r)(E,1)/r!
Ω	1.5311305564603	Real period
R	1.5277076804621	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	24400h1 97600be1 109800x1 12200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12200k1

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

---

Quadratic twists for elliptic curve 12200k1

-4	8	-3	5
24400h1	97600be1	109800x1	12200c1

---

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