Cremona's table of elliptic curves

1938 = 2 · 3 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 17- 19+	Signs for the Atkin-Lehner involutions
Class	1938f	Isogeny class
Conductor	1938	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	15504 = 24 · 3 · 17 · 19	Discriminant
Eigenvalues	2+ 3- -2  0  4 -6 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-22,-40]	[a1,a2,a3,a4,a6]
Generators	[6:4:1]	Generators of the group modulo torsion
j	1102302937/15504	j-invariant
L	2.4065729334887	L(r)(E,1)/r!
Ω	2.2184752848196	Real period
R	2.1695738058983	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	15504r1 62016q1 5814p1 48450w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938f1

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

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Quadratic twists for elliptic curve 1938f1

-4	8	-3	5	-7	17	-19
15504r1	62016q1	5814p1	48450w1	94962i1	32946b1	36822u1

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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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