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	12432bz	Isogeny class
Conductor	12432	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	29473984512 = 212 · 34 · 74 · 37	Discriminant
Eigenvalues	2- 3- -2 7- -4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3304,71540]	[a1,a2,a3,a4,a6]
Generators	[-28:378:1]	Generators of the group modulo torsion
j	974126411497/7195797	j-invariant
L	4.9128616051903	L(r)(E,1)/r!
Ω	1.1841377121819	Real period
R	1.0372234484741	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	777a3 49728dn4 37296co4 87024ct4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bz3

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

---

Quadratic twists for elliptic curve 12432bz3

-4	8	-3	-7
777a3	49728dn4	37296co4	87024ct4

---

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