Cremona's table of elliptic curves

40368 = 2⁴ · 3 · 29²

Field	Data	Notes
Atkin-Lehner	2- 3+ 29-	Signs for the Atkin-Lehner involutions
Class	40368bb	Isogeny class
Conductor	40368	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-3318096524544 = -1 · 28 · 312 · 293	Discriminant
Eigenvalues	2- 3+  2 -4 -4 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6892,-234740]	[a1,a2,a3,a4,a6]
Generators	[30285990290:-621808282503:68921000]	Generators of the group modulo torsion
j	-5799473552/531441	j-invariant
L	3.8901443807707	L(r)(E,1)/r!
Ω	0.26062598922297	Real period
R	14.926156797986	Regulator
r	1	Rank of the group of rational points
S	0.99999999999957	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10092j2 121104cx2 40368bq2	Quadratic twists by: -4 -3 29

Hecke Eigenvalues for elliptic curve 40368bb2

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	-4	-2	4	-4	0	-	4	-8	4	12	-12	2	-4	8	8	-8	8	4	4	-4	8

---

Quadratic twists for elliptic curve 40368bb2

-4	-3	29
10092j2	121104cx2	40368bq2

---

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