Cremona's table of elliptic curves

8736 = 2⁵ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	8736b	Isogeny class
Conductor	8736	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-1913393664 = -1 · 29 · 35 · 7 · 133	Discriminant
Eigenvalues	2+ 3+  3 7+ -5 13+  1  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,296,676]	[a1,a2,a3,a4,a6]
Generators	[0:26:1]	Generators of the group modulo torsion
j	5582912824/3737097	j-invariant
L	4.1408240011174	L(r)(E,1)/r!
Ω	0.92952937349201	Real period
R	2.2273766269275	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8736x1 17472be1 26208bi1 61152z1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736b1

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
+	+	3	+	-5	+	1	5	-3	1	0	-3	-4	-11	8	6	12	13	-2	-8	7	-14	-6	-6	-6

---

Quadratic twists for elliptic curve 8736b1

-4	8	-3	-7	13
8736x1	17472be1	26208bi1	61152z1	113568cc1

---

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