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	4704bc	Isogeny class
Conductor	4704	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	69731032896 = 26 · 33 · 79	Discriminant
Eigenvalues	2- 3-  2 7-  2  0  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12462,531180]	[a1,a2,a3,a4,a6]
j	82881856/27	j-invariant
L	3.2226158298152	L(r)(E,1)/r!
Ω	1.0742052766051	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	4704e1 9408m2 14112y1 117600q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4704bc1

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	0	2	0	-2	6	4	6	-2	0	0	-6	-12	12	12	10	12	-12	-12	14	-12

---

Quadratic twists for elliptic curve 4704bc1

-4	8	-3	5	-7
4704e1	9408m2	14112y1	117600q1	4704w1

---

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