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	12200c	Isogeny class
Conductor	12200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	30500000000 = 28 · 59 · 61	Discriminant
Eigenvalues	2+  0 5-  0  6  4 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2375,-43750]	[a1,a2,a3,a4,a6]
j	2963088/61	j-invariant
L	2.7389696053379	L(r)(E,1)/r!
Ω	0.68474240133448	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24400g1 97600bf1 109800cb1 12200k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12200c1

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 12200c1

-4	8	-3	5
24400g1	97600bf1	109800cb1	12200k1

---

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