Cremona's table of elliptic curves

12992 = 2⁶ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	12992bf	Isogeny class
Conductor	12992	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-4726177792 = -1 · 214 · 73 · 292	Discriminant
Eigenvalues	2- -2  2 7+  0 -2  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,303,-2513]	[a1,a2,a3,a4,a6]
Generators	[9:32:1]	Generators of the group modulo torsion
j	187153328/288463	j-invariant
L	3.5466170480275	L(r)(E,1)/r!
Ω	0.72519035790551	Real period
R	2.445300747152	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	12992s1 3248a1 116928dm1 90944ee1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992bf1

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	+	0	-2	0	6	8	-	-6	-10	-12	4	-6	10	-8	12	-12	0	-16	8	12	0	8

---

Quadratic twists for elliptic curve 12992bf1

-4	8	-3	-7
12992s1	3248a1	116928dm1	90944ee1

---

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