Cremona's table of elliptic curves

122694 = 2 · 3 · 11² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 13+	Signs for the Atkin-Lehner involutions
Class	122694bf	Isogeny class
Conductor	122694	Conductor
∏ cp	66	Product of Tamagawa factors cp
deg	2407680	Modular degree for the optimal curve
Δ	197190506678307714 = 2 · 311 · 117 · 134	Discriminant
Eigenvalues	2+ 3-  1 -2 11- 13+ -7  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-685468,217333664]	[a1,a2,a3,a4,a6]
Generators	[274:-7216:1]	Generators of the group modulo torsion
j	703971110401/3897234	j-invariant
L	6.0775901299937	L(r)(E,1)/r!
Ω	0.31963652983913	Real period
R	0.28809191028559	Regulator
r	1	Rank of the group of rational points
S	1.000000005005	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11154bh1 122694da1	Quadratic twists by: -11 13

Hecke Eigenvalues for elliptic curve 122694bf1

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	-2	-	+	-7	7	8	-6	3	2	-10	4	-6	1	1	-1	-14	4	16	8	-2	6	-3

---

Quadratic twists for elliptic curve 122694bf1

-11	13
11154bh1	122694da1

---

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