Cremona's table of elliptic curves

121296 = 2⁴ · 3 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 19-	Signs for the Atkin-Lehner involutions
Class	121296dj	Isogeny class
Conductor	121296	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	1382400	Modular degree for the optimal curve
Δ	174380331766136832 = 214 · 35 · 72 · 197	Discriminant
Eigenvalues	2- 3- -2 7-  2 -2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-528624,146387412]	[a1,a2,a3,a4,a6]
Generators	[348:2166:1]	Generators of the group modulo torsion
j	84778086457/904932	j-invariant
L	7.2228195168597	L(r)(E,1)/r!
Ω	0.32257244313058	Real period
R	0.55978274363579	Regulator
r	1	Rank of the group of rational points
S	1.0000000037911	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15162s1 6384x1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 121296dj1

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

---

Quadratic twists for elliptic curve 121296dj1

-4	-19
15162s1	6384x1

---

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