Cremona's table of elliptic curves

12936 = 2³ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	12936d	Isogeny class
Conductor	12936	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	-121011701258714112 = -1 · 210 · 34 · 77 · 116	Discriminant
Eigenvalues	2+ 3+  4 7- 11+  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-164656,30738268]	[a1,a2,a3,a4,a6]
j	-4097989445764/1004475087	j-invariant
L	2.5241815999708	L(r)(E,1)/r!
Ω	0.31552269999635	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872z1 103488en1 38808cq1 1848e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12936d1

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

---

Quadratic twists for elliptic curve 12936d1

-4	8	-3	-7
25872z1	103488en1	38808cq1	1848e1

---

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