Cremona's table of elliptic curves

8712 = 2³ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+	Signs for the Atkin-Lehner involutions
Class	8712a	Isogeny class
Conductor	8712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	130385075521536 = 211 · 33 · 119	Discriminant
Eigenvalues	2+ 3+  2 -2 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-171699,27378670]	[a1,a2,a3,a4,a6]
Generators	[83454:27560:343]	Generators of the group modulo torsion
j	4293378	j-invariant
L	4.6154420587322	L(r)(E,1)/r!
Ω	0.57008737089234	Real period
R	8.0960257925163	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424a2 69696d2 8712p2 8712o2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8712a2

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

---

Quadratic twists for elliptic curve 8712a2

-4	8	-3	-11
17424a2	69696d2	8712p2	8712o2

---

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