Cremona's table of elliptic curves

12274 = 2 · 17 · 19²

Field	Data	Notes
Atkin-Lehner	2- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	12274m	Isogeny class
Conductor	12274	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	18478116588608 = 26 · 17 · 198	Discriminant
Eigenvalues	2-  0  4 -2  4 -6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-45193,3703369]	[a1,a2,a3,a4,a6]
Generators	[1069:33760:1]	Generators of the group modulo torsion
j	216973458729/392768	j-invariant
L	8.115764097183	L(r)(E,1)/r!
Ω	0.68905662782114	Real period
R	1.9630133357945	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	98192l1 110466y1 646a1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 12274m1

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	4	-2	4	-6	+	-	-6	0	-6	4	-6	-4	0	-14	4	0	-4	-10	10	10	-12	-14	10

---

Quadratic twists for elliptic curve 12274m1

-4	-3	-19
98192l1	110466y1	646a1

---

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