Cremona's table of elliptic curves

76050 = 2 · 3² · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	76050ek	Isogeny class
Conductor	76050	Conductor
∏ cp	30	Product of Tamagawa factors cp
Δ	-2882554889011200 = -1 · 215 · 36 · 52 · 136	Discriminant
Eigenvalues	2- 3- 5+  2 -3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,33430,1058217]	[a1,a2,a3,a4,a6]
Generators	[465:10583:1]	Generators of the group modulo torsion
j	46969655/32768	j-invariant
L	10.294884420534	L(r)(E,1)/r!
Ω	0.28601151684899	Real period
R	1.1998216639318	Regulator
r	1	Rank of the group of rational points
S	0.99999999990783	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8450d2 76050cr4 450d2	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 76050ek2

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	-3	+	-3	-5	6	0	-2	2	-3	4	-12	6	0	2	-13	12	11	-10	9	15	2

---

Quadratic twists for elliptic curve 76050ek2

-3	5	13
8450d2	76050cr4	450d2

---

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