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	69696eo	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	1571086281904128 = 212 · 39 · 117	Discriminant
Eigenvalues	2- 3+  2 -4 11-  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39204,-2299968]	[a1,a2,a3,a4,a6]
Generators	[906:26568:1]	Generators of the group modulo torsion
j	46656/11	j-invariant
L	5.8458699067933	L(r)(E,1)/r!
Ω	0.34507321594541	Real period
R	4.2352388099038	Regulator
r	1	Rank of the group of rational points
S	1.0000000001834	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696en1 34848bn1 69696es1 6336bk1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696eo1

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

---

Quadratic twists for elliptic curve 69696eo1

-4	8	-3	-11
69696en1	34848bn1	69696es1	6336bk1

---

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