Cremona's table of elliptic curves

27048 = 2³ · 3 · 7² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 23-	Signs for the Atkin-Lehner involutions
Class	27048v	Isogeny class
Conductor	27048	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	910255485791232 = 210 · 33 · 76 · 234	Discriminant
Eigenvalues	2- 3- -2 7- -4  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36864,-2317680]	[a1,a2,a3,a4,a6]
Generators	[-96:588:1]	Generators of the group modulo torsion
j	45989074372/7555707	j-invariant
L	5.3933227817697	L(r)(E,1)/r!
Ω	0.34838557822549	Real period
R	1.2900751157287	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	54096f4 81144q4 552d3	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 27048v4

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

---

Quadratic twists for elliptic curve 27048v4

-4	-3	-7
54096f4	81144q4	552d3

---

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