Cremona's table of elliptic curves

12432 = 2⁴ · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 37-	Signs for the Atkin-Lehner involutions
Class	12432bd	Isogeny class
Conductor	12432	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	7723220136912 = 24 · 34 · 76 · 373	Discriminant
Eigenvalues	2- 3+  0 7+  0 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17913,919044]	[a1,a2,a3,a4,a6]
Generators	[-60:1332:1]	Generators of the group modulo torsion
j	39731316127744000/482701258557	j-invariant
L	3.6080137058693	L(r)(E,1)/r!
Ω	0.74331741269069	Real period
R	1.61797801956	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	3108i3 49728dx3 37296bw3 87024dz3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bd3

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

---

Quadratic twists for elliptic curve 12432bd3

-4	8	-3	-7
3108i3	49728dx3	37296bw3	87024dz3

---

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