Cremona's table of elliptic curves

1558 = 2 · 19 · 41

Field	Data	Notes
Atkin-Lehner	2+ 19- 41+	Signs for the Atkin-Lehner involutions
Class	1558a	Isogeny class
Conductor	1558	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-58469108678494208 = -1 · 211 · 198 · 412	Discriminant
Eigenvalues	2+  0 -2 -2  0 -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-100393,-16864179]	[a1,a2,a3,a4,a6]
j	-111901637620233904617/58469108678494208	j-invariant
L	0.52355473773742	L(r)(E,1)/r!
Ω	0.13088868443436	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	12464b2 49856a2 14022j2 38950s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1558a2

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

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Quadratic twists for elliptic curve 1558a2

-4	8	-3	5	-7	-19	41
12464b2	49856a2	14022j2	38950s2	76342b2	29602e2	63878a2

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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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