Cremona's table of elliptic curves

42432 = 2⁶ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 17-	Signs for the Atkin-Lehner involutions
Class	42432bo	Isogeny class
Conductor	42432	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	553992192 = 214 · 32 · 13 · 172	Discriminant
Eigenvalues	2- 3+ -2  2  4 13+ 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-209,-207]	[a1,a2,a3,a4,a6]
Generators	[-13:12:1]	Generators of the group modulo torsion
j	61918288/33813	j-invariant
L	4.5307496892254	L(r)(E,1)/r!
Ω	1.3401640190795	Real period
R	1.6903713369127	Regulator
r	1	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42432u2 10608j2 127296cb2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 42432bo2

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	4	+	-	-8	0	-2	6	4	2	-4	6	-6	-10	10	4	-8	0	4	14	16	-12

---

Quadratic twists for elliptic curve 42432bo2

-4	8	-3
42432u2	10608j2	127296cb2

---

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