Cremona's table of elliptic curves

4704 = 2⁵ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7-	Signs for the Atkin-Lehner involutions
Class	4704s	Isogeny class
Conductor	4704	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	30359089152 = 212 · 32 · 77	Discriminant
Eigenvalues	2- 3+  0 7-  2  2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1633,24529]	[a1,a2,a3,a4,a6]
Generators	[-9:196:1]	Generators of the group modulo torsion
j	1000000/63	j-invariant
L	3.2775811521616	L(r)(E,1)/r!
Ω	1.1547699081406	Real period
R	0.70957450680351	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	4704l2 9408ba1 14112p2 117600cw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704s2

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
-	+	0	-	2	2	-4	-4	6	-2	0	-6	-8	8	-4	-6	0	14	-4	2	2	-4	12	0	-6

---

Quadratic twists for elliptic curve 4704s2

-4	8	-3	5	-7
4704l2	9408ba1	14112p2	117600cw2	672g2

---

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