Cremona's table of elliptic curves

27840 = 2⁶ · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	27840cb	Isogeny class
Conductor	27840	Conductor
∏ cp	392	Product of Tamagawa factors cp
deg	451584	Modular degree for the optimal curve
Δ	44385952320000000 = 212 · 314 · 57 · 29	Discriminant
Eigenvalues	2+ 3- 5- -2 -2  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3026665,2025690263]	[a1,a2,a3,a4,a6]
Generators	[971:-1800:1]	Generators of the group modulo torsion
j	748612322643635839936/10836414140625	j-invariant
L	6.4401140197534	L(r)(E,1)/r!
Ω	0.32883317927314	Real period
R	0.19984433847708	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	27840u1 13920t1 83520bo1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27840cb1

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

---

Quadratic twists for elliptic curve 27840cb1

-4	8	-3
27840u1	13920t1	83520bo1

---

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