Cremona's table of elliptic curves

122304 = 2⁶ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	122304hy	Isogeny class
Conductor	122304	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	3870720	Modular degree for the optimal curve
Δ	-8.4838463560268E+20	Discriminant
Eigenvalues	2- 3- -1 7-  1 13- -5  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1039519,-1340339169]	[a1,a2,a3,a4,a6]
Generators	[8983:856128:1]	Generators of the group modulo torsion
j	11743520417/80199288	j-invariant
L	8.2875682978282	L(r)(E,1)/r!
Ω	0.07891472108474	Real period
R	0.87516078051331	Regulator
r	1	Rank of the group of rational points
S	1.0000000036207	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122304bs1 30576bn1 122304ex1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304hy1

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	-	1	-	-5	1	5	3	-2	11	0	-1	12	-10	-14	1	4	2	1	8	2	12	2

---

Quadratic twists for elliptic curve 122304hy1

-4	8	-7
122304bs1	30576bn1	122304ex1

---

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