Cremona's table of elliptic curves

69696 = 2⁶ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	69696cl	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	126956467224576 = 215 · 37 · 116	Discriminant
Eigenvalues	2+ 3-  2  4 11- -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-140844,20337680]	[a1,a2,a3,a4,a6]
Generators	[-22:4840:1]	Generators of the group modulo torsion
j	7301384/3	j-invariant
L	8.4831078867942	L(r)(E,1)/r!
Ω	0.57676737888305	Real period
R	1.8385028776371	Regulator
r	1	Rank of the group of rational points
S	1.000000000043	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696co4 34848ba4 23232u4 576c3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696cl4

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

---

Quadratic twists for elliptic curve 69696cl4

-4	8	-3	-11
69696co4	34848ba4	23232u4	576c3

---

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