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	12992u	Isogeny class
Conductor	12992	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	372506624 = 218 · 72 · 29	Discriminant
Eigenvalues	2+ -2 -2 7-  4  2  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9889,375231]	[a1,a2,a3,a4,a6]
Generators	[50:91:1]	Generators of the group modulo torsion
j	408023180713/1421	j-invariant
L	3.0431147915581	L(r)(E,1)/r!
Ω	1.4839388163276	Real period
R	2.0507009844847	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	12992be2 203c2 116928cb2 90944ca2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992u2

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

---

Quadratic twists for elliptic curve 12992u2

-4	8	-3	-7
12992be2	203c2	116928cb2	90944ca2

---

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