Cremona's table of elliptic curves

12138 = 2 · 3 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	12138w	Isogeny class
Conductor	12138	Conductor
∏ cp	768	Product of Tamagawa factors cp
deg	1105920	Modular degree for the optimal curve
Δ	1.338873434519E+21	Discriminant
Eigenvalues	2- 3-  2 7+ -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-20300522,35159634852]	[a1,a2,a3,a4,a6]
Generators	[628:150214:1]	Generators of the group modulo torsion
j	38331145780597164097/55468445663232	j-invariant
L	8.7524438962465	L(r)(E,1)/r!
Ω	0.15220804312798	Real period
R	1.1979825600838	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	97104cb1 36414t1 84966da1 714g1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138w1

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

---

Quadratic twists for elliptic curve 12138w1

-4	-3	-7	17
97104cb1	36414t1	84966da1	714g1

---

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