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	12432i	Isogeny class
Conductor	12432	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7168	Modular degree for the optimal curve
Δ	-198713088 = -1 · 28 · 34 · 7 · 372	Discriminant
Eigenvalues	2+ 3- -4 7+ -4 -4 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,140,284]	[a1,a2,a3,a4,a6]
Generators	[-1:12:1] [2:24:1]	Generators of the group modulo torsion
j	1176960944/776223	j-invariant
L	5.9790725384917	L(r)(E,1)/r!
Ω	1.1196095278426	Real period
R	1.335079862623	Regulator
r	2	Rank of the group of rational points
S	0.99999999999965	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6216p1 49728di1 37296l1 87024l1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432i1

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

---

Quadratic twists for elliptic curve 12432i1

-4	8	-3	-7
6216p1	49728di1	37296l1	87024l1

---

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