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	69696cw	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1.97911624235E+21	Discriminant
Eigenvalues	2+ 3- -2 -4 11- -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,3030324,677319280]	[a1,a2,a3,a4,a6]
Generators	[2484:153400:1]	Generators of the group modulo torsion
j	9090072503/5845851	j-invariant
L	2.7613681616337	L(r)(E,1)/r!
Ω	0.091991089962878	Real period
R	7.5044446214525	Regulator
r	1	Rank of the group of rational points
S	1.0000000001665	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696gp3 1089g4 23232ca3 6336bd4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696cw3

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

---

Quadratic twists for elliptic curve 69696cw3

-4	8	-3	-11
69696gp3	1089g4	23232ca3	6336bd4

---

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