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	122304ie	Isogeny class
Conductor	122304	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1733473064787050496 = 216 · 3 · 714 · 13	Discriminant
Eigenvalues	2- 3-  2 7-  0 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-319937,28858815]	[a1,a2,a3,a4,a6]
Generators	[250871343162471:-10354866145989420:134453795867]	Generators of the group modulo torsion
j	469732169092/224827239	j-invariant
L	11.355452142769	L(r)(E,1)/r!
Ω	0.23634261331103	Real period
R	24.023285484005	Regulator
r	1	Rank of the group of rational points
S	0.99999999996091	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	122304bw3 30576e3 17472cf3	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ie3

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

---

Quadratic twists for elliptic curve 122304ie3

-4	8	-7
122304bw3	30576e3	17472cf3

---

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