Cremona's table of elliptic curves

380 = 2² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	380a	Isogeny class
Conductor	380	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	28880 = 24 · 5 · 192	Discriminant
Eigenvalues	2-  0 5+ -2 -4 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8,-3]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	3538944/1805	j-invariant
L	1.6365169446457	L(r)(E,1)/r!
Ω	2.9974122711911	Real period
R	1.0919531893391	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1520f1 6080g1 3420d1 1900c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 380a1

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	+	-2	-4	-4	6	-	-2	-6	-8	4	6	-6	6	8	-12	6	0	0	-10	-8	14	14	16

---

Quadratic twists for elliptic curve 380a1

-4	8	-3	5	-7	-11	13	17	-19
1520f1	6080g1	3420d1	1900c1	18620j1	45980a1	64220h1	109820k1	7220b1

---

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