Cremona's table of elliptic curves

4700 = 2² · 5² · 47

Field	Data	Notes
Atkin-Lehner	2- 5+ 47-	Signs for the Atkin-Lehner involutions
Class	4700f	Isogeny class
Conductor	4700	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	23500000000 = 28 · 59 · 47	Discriminant
Eigenvalues	2- -3 5+  3  5 -5  2  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2575,49750]	[a1,a2,a3,a4,a6]
Generators	[-5:250:1]	Generators of the group modulo torsion
j	472058064/5875	j-invariant
L	2.6170229881238	L(r)(E,1)/r!
Ω	1.2046109448363	Real period
R	0.18104206170893	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	18800x1 75200ba1 42300s1 940b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4700f1

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	+	3	5	-5	2	1	-4	-8	-5	-2	6	-6	-	-8	0	5	4	-16	11	-4	-11	-10	2

---

Quadratic twists for elliptic curve 4700f1

-4	8	-3	5
18800x1	75200ba1	42300s1	940b1

---

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