Cremona's table of elliptic curves

4758 = 2 · 3 · 13 · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 61-	Signs for the Atkin-Lehner involutions
Class	4758h	Isogeny class
Conductor	4758	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	10599672564 = 22 · 32 · 136 · 61	Discriminant
Eigenvalues	2- 3- -2 -2 -4 13+ -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1164,14364]	[a1,a2,a3,a4,a6]
j	174423891623617/10599672564	j-invariant
L	2.5231642354195	L(r)(E,1)/r!
Ω	1.2615821177097	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	38064s2 14274h2 118950i2 61854j2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4758h2

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	-4	+	-4	0	6	8	10	8	6	-4	8	0	0	-	-6	12	14	4	-4	14	10

---

Quadratic twists for elliptic curve 4758h2

-4	-3	5	13
38064s2	14274h2	118950i2	61854j2

---

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