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	122304ik	Isogeny class
Conductor	122304	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	2909098999812096 = 212 · 36 · 78 · 132	Discriminant
Eigenvalues	2- 3-  2 7- -4 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-35737,-178585]	[a1,a2,a3,a4,a6]
Generators	[-109:1560:1]	Generators of the group modulo torsion
j	10474708672/6036849	j-invariant
L	10.032539693995	L(r)(E,1)/r!
Ω	0.37828918961031	Real period
R	2.2100683666712	Regulator
r	1	Rank of the group of rational points
S	1.0000000036937	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	122304gd2 61152e1 17472cg2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ik2

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
-	-	2	-	-4	-	-6	4	8	6	0	-10	10	8	0	-10	0	-2	-4	-12	-14	0	-16	10	2

---

Quadratic twists for elliptic curve 122304ik2

-4	8	-7
122304gd2	61152e1	17472cg2

---

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