Cremona's table of elliptic curves

76 = 2² · 19

Field	Data	Notes
Atkin-Lehner	2- 19+	Signs for the Atkin-Lehner involutions
Class	76a	Isogeny class
Conductor	76	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-4864 = -1 · 28 · 19	Discriminant
Eigenvalues	2-  2 -1 -3  5 -4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21,-31]	[a1,a2,a3,a4,a6]
j	-4194304/19	j-invariant
L	1.1104197465123	L(r)(E,1)/r!
Ω	1.1104197465123	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	304f1 1216h1 684a1 1900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 76a1

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	-1	-3	5	-4	-3	+	8	-2	4	10	10	1	-1	-4	6	-13	-12	2	9	8	-12	12	-8

---

Quadratic twists for elliptic curve 76a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
304f1	1216h1	684a1	1900b1	3724b1	9196g1	12844d1	21964c1	1444c1	40204i1	63916f1	73036a1	104044d1	127756b1

---

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