Cremona's table of elliptic curves

123840 = 2⁶ · 3² · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 43-	Signs for the Atkin-Lehner involutions
Class	123840fr	Isogeny class
Conductor	123840	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-4212073820160000 = -1 · 215 · 314 · 54 · 43	Discriminant
Eigenvalues	2- 3- 5+ -4  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7788,3133712]	[a1,a2,a3,a4,a6]
Generators	[-158:648:1] [-14:1800:1]	Generators of the group modulo torsion
j	-2186875592/176326875	j-invariant
L	9.8049786446759	L(r)(E,1)/r!
Ω	0.36090657539067	Real period
R	3.3959545605336	Regulator
r	2	Rank of the group of rational points
S	0.99999999996735	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123840eu3 61920bz2 41280cs3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 123840fr3

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

---

Quadratic twists for elliptic curve 123840fr3

-4	8	-3
123840eu3	61920bz2	41280cs3

---

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