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	12992f	Isogeny class
Conductor	12992	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-77433696944128 = -1 · 228 · 73 · 292	Discriminant
Eigenvalues	2+  0  0 7+  4  0 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19340,1118448]	[a1,a2,a3,a4,a6]
j	-3051779837625/295386112	j-invariant
L	1.1932917061589	L(r)(E,1)/r!
Ω	0.59664585307947	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12992bi1 406a1 116928x1 90944bj1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992f1

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

---

Quadratic twists for elliptic curve 12992f1

-4	8	-3	-7
12992bi1	406a1	116928x1	90944bj1

---

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