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	380b	Isogeny class
Conductor	380	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	6516050000 = 24 · 55 · 194	Discriminant
Eigenvalues	2-  2 5+  2  0  6  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-921,10346]	[a1,a2,a3,a4,a6]
j	5405726654464/407253125	j-invariant
L	1.9610721647212	L(r)(E,1)/r!
Ω	1.3073814431474	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	1520i1 6080j1 3420a1 1900a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 380b1

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

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Quadratic twists for elliptic curve 380b1

-4	8	-3	5	-7	-11	13	17	-19
1520i1	6080j1	3420a1	1900a1	18620q1	45980c1	64220n1	109820i1	7220d1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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