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	69696ff	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-46356756627456 = -1 · 216 · 312 · 113	Discriminant
Eigenvalues	2- 3- -2  2 11+ -4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,4884,-300080]	[a1,a2,a3,a4,a6]
Generators	[48:212:1]	Generators of the group modulo torsion
j	202612/729	j-invariant
L	5.1625029058802	L(r)(E,1)/r!
Ω	0.32454527160822	Real period
R	3.9767201665454	Regulator
r	1	Rank of the group of rational points
S	0.99999999992924	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696be2 17424i2 23232dh2 69696fg2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ff2

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

---

Quadratic twists for elliptic curve 69696ff2

-4	8	-3	-11
69696be2	17424i2	23232dh2	69696fg2

---

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