Cremona's table of elliptic curves

4641 = 3 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3- 7- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	4641f	Isogeny class
Conductor	4641	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2208	Modular degree for the optimal curve
Δ	-40000779 = -1 · 32 · 7 · 133 · 172	Discriminant
Eigenvalues	-2 3-  3 7- -6 13+ 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-14,-310]	[a1,a2,a3,a4,a6]
Generators	[10:25:1]	Generators of the group modulo torsion
j	-325660672/40000779	j-invariant
L	2.713255172384	L(r)(E,1)/r!
Ω	0.90600763540451	Real period
R	0.74868441124466	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	74256bj1 13923k1 116025h1 32487i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4641f1

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	-	3	-	-6	+	+	-1	-5	-1	1	2	-6	-5	7	5	4	10	-8	-10	7	-11	-9	-5	-13

---

Quadratic twists for elliptic curve 4641f1

-4	-3	5	-7	13	17
74256bj1	13923k1	116025h1	32487i1	60333j1	78897a1

---

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