Cremona's table of elliptic curves

840 = 2³ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	840i	Isogeny class
Conductor	840	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	26880 = 28 · 3 · 5 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7-  0  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36,-96]	[a1,a2,a3,a4,a6]
j	20720464/105	j-invariant
L	1.9451617257878	L(r)(E,1)/r!
Ω	1.9451617257878	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1680a1 6720k1 2520i1 4200a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840i1

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
-	-	+	-	0	2	2	4	0	2	4	2	-2	8	-4	-2	12	-14	8	-8	-2	8	-4	-18	-2

---

Quadratic twists for elliptic curve 840i1

-4	8	-3	5	-7	-11
1680a1	6720k1	2520i1	4200a1	5880x1	101640t1

---

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