Cremona's table of elliptic curves

12104 = 2³ · 17 · 89

Field	Data	Notes
Atkin-Lehner	2- 17- 89+	Signs for the Atkin-Lehner involutions
Class	12104c	Isogeny class
Conductor	12104	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1664	Modular degree for the optimal curve
Δ	6584576 = 28 · 172 · 89	Discriminant
Eigenvalues	2-  2  2 -2  0 -2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-52,-60]	[a1,a2,a3,a4,a6]
Generators	[12:30:1]	Generators of the group modulo torsion
j	61918288/25721	j-invariant
L	6.8780749358951	L(r)(E,1)/r!
Ω	1.8414675851269	Real period
R	1.8675525410948	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	24208c1 96832i1 108936e1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12104c1

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

---

Quadratic twists for elliptic curve 12104c1

-4	8	-3
24208c1	96832i1	108936e1

---

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