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	12138m	Isogeny class
Conductor	12138	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	387072	Modular degree for the optimal curve
Δ	-1.5129568665742E+19	Discriminant
Eigenvalues	2+ 3- -2 7-  6  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-963677,409316600]	[a1,a2,a3,a4,a6]
Generators	[-690:27655:1]	Generators of the group modulo torsion
j	-4100379159705193/626805817344	j-invariant
L	4.0667549346711	L(r)(E,1)/r!
Ω	0.21379257980641	Real period
R	0.39629093402445	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	97104bm1 36414ct1 84966u1 714a1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138m1

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

---

Quadratic twists for elliptic curve 12138m1

-4	-3	-7	17
97104bm1	36414ct1	84966u1	714a1

---

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