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	12138g	Isogeny class
Conductor	12138	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	587520	Modular degree for the optimal curve
Δ	-2.440654698342E+19	Discriminant
Eigenvalues	2+ 3- -1 7+ -5 -1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4218684,-3343946630]	[a1,a2,a3,a4,a6]
j	-344002044213921241/1011143540736	j-invariant
L	0.31597310811267	L(r)(E,1)/r!
Ω	0.052662184685446	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	97104bx1 36414cg1 84966o1 714c1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138g1

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
+	-	-1	+	-5	-1	+	-6	-6	-6	-4	-11	0	-9	4	-7	12	-6	13	-4	13	-15	13	13	9

---

Quadratic twists for elliptic curve 12138g1

-4	-3	-7	17
97104bx1	36414cg1	84966o1	714c1

---

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