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	69696ef	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	7.0786863517472E+19	Discriminant
Eigenvalues	2- 3+  0  2 11-  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-71416620,-232298492976]	[a1,a2,a3,a4,a6]
Generators	[256877641020:19069877445256:20346417]	Generators of the group modulo torsion
j	4406910829875/7744	j-invariant
L	6.9379994222479	L(r)(E,1)/r!
Ω	0.051933761294718	Real period
R	16.699154965113	Regulator
r	1	Rank of the group of rational points
S	0.99999999999921	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696l4 17424bd4 69696ee2 6336bp4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ef4

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

---

Quadratic twists for elliptic curve 69696ef4

-4	8	-3	-11
69696l4	17424bd4	69696ee2	6336bp4

---

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