Cremona's table of elliptic curves

26508 = 2² · 3 · 47²

Field	Data	Notes
Atkin-Lehner	2- 3+ 47-	Signs for the Atkin-Lehner involutions
Class	26508c	Isogeny class
Conductor	26508	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	137088	Modular degree for the optimal curve
Δ	3432376100646144 = 28 · 317 · 473	Discriminant
Eigenvalues	2- 3+ -3  3  1  2  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-51637,3546049]	[a1,a2,a3,a4,a6]
Generators	[72:443:1]	Generators of the group modulo torsion
j	572903653376/129140163	j-invariant
L	4.3970044980916	L(r)(E,1)/r!
Ω	0.41993649587618	Real period
R	5.235320746435	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	106032bn1 79524i1 26508b1	Quadratic twists by: -4 -3 -47

Hecke Eigenvalues for elliptic curve 26508c1

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
-	+	-3	3	1	2	2	2	3	1	2	-3	-10	10	-	-6	2	-10	8	-12	-8	-5	14	-4	1

---

Quadratic twists for elliptic curve 26508c1

-4	-3	-47
106032bn1	79524i1	26508b1

---

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