Cremona's table of elliptic curves

36192 = 2⁵ · 3 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13- 29+	Signs for the Atkin-Lehner involutions
Class	36192j	Isogeny class
Conductor	36192	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-14122987008 = -1 · 29 · 3 · 13 · 294	Discriminant
Eigenvalues	2+ 3+ -2 -4  0 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,136,5640]	[a1,a2,a3,a4,a6]
Generators	[1:76:1] [85:790:1]	Generators of the group modulo torsion
j	539353144/27583959	j-invariant
L	6.0867103473665	L(r)(E,1)/r!
Ω	0.95155913289889	Real period
R	12.793131056023	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	36192s2 72384da3 108576bp2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 36192j2

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

---

Quadratic twists for elliptic curve 36192j2

-4	8	-3
36192s2	72384da3	108576bp2

---

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