Cremona's table of elliptic curves

4270 = 2 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 61-	Signs for the Atkin-Lehner involutions
Class	4270h	Isogeny class
Conductor	4270	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-6784462090000 = -1 · 24 · 54 · 72 · 614	Discriminant
Eigenvalues	2-  0 5- 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,2243,-119019]	[a1,a2,a3,a4,a6]
j	1248512920207839/6784462090000	j-invariant
L	3.005569741764	L(r)(E,1)/r!
Ω	0.3756962177205	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	34160bd3 38430g3 21350g3 29890m3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4270h4

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	-	+	0	-2	2	4	0	6	4	6	-6	-4	4	6	0	-	12	4	2	-4	8	18	10

---

Quadratic twists for elliptic curve 4270h4

-4	-3	5	-7
34160bd3	38430g3	21350g3	29890m3

---

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