Cremona's table of elliptic curves

15162 = 2 · 3 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	15162z	Isogeny class
Conductor	15162	Conductor
∏ cp	1232	Product of Tamagawa factors cp
deg	492800	Modular degree for the optimal curve
Δ	1.5981979284026E+19	Discriminant
Eigenvalues	2- 3-  0 7+  4  2 -8 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-796478,194507844]	[a1,a2,a3,a4,a6]
Generators	[220:5362:1]	Generators of the group modulo torsion
j	8146748259978623875/2330074250477568	j-invariant
L	8.8765435568738	L(r)(E,1)/r!
Ω	0.20510120382851	Real period
R	0.14051573601354	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	121296bx1 45486d1 106134bs1 15162a1	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 15162z1

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

---

Quadratic twists for elliptic curve 15162z1

-4	-3	-7	-19
121296bx1	45486d1	106134bs1	15162a1

---

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