Cremona's table of elliptic curves

3640 = 2³ · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 13-	Signs for the Atkin-Lehner involutions
Class	3640j	Isogeny class
Conductor	3640	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	12800	Modular degree for the optimal curve
Δ	59953930400000 = 28 · 55 · 78 · 13	Discriminant
Eigenvalues	2- -2 5- 7- -2 13- -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10340,-161600]	[a1,a2,a3,a4,a6]
Generators	[-30:350:1]	Generators of the group modulo torsion
j	477625344356176/234195040625	j-invariant
L	2.6951456120985	L(r)(E,1)/r!
Ω	0.49761985017904	Real period
R	0.13540183390638	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	7280g1 29120h1 32760l1 18200b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3640j1

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	-	-6	6	6	-6	-10	-6	10	2	0	-10	-14	2	16	6	-2	4	4	2	-14

---

Quadratic twists for elliptic curve 3640j1

-4	8	-3	5	-7	13
7280g1	29120h1	32760l1	18200b1	25480k1	47320c1

---

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