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	1938c	Isogeny class
Conductor	1938	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	269893632 = 214 · 3 · 172 · 19	Discriminant
Eigenvalues	2+ 3+  0  0  4  4 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-300,-1968]	[a1,a2,a3,a4,a6]
j	3001563015625/269893632	j-invariant
L	1.1532408843351	L(r)(E,1)/r!
Ω	1.1532408843351	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	15504s1 62016s1 5814s1 48450bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938c1

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

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Quadratic twists for elliptic curve 1938c1

-4	8	-3	5	-7	17	-19
15504s1	62016s1	5814s1	48450bw1	94962u1	32946j1	36822x1

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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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