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	1558b	Isogeny class
Conductor	1558	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	252	Modular degree for the optimal curve
Δ	-99712 = -1 · 27 · 19 · 41	Discriminant
Eigenvalues	2+  0  4  4 -3 -4  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,10,-12]	[a1,a2,a3,a4,a6]
j	104487111/99712	j-invariant
L	1.8376978437819	L(r)(E,1)/r!
Ω	1.8376978437819	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12464c1 49856b1 14022k1 38950t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1558b1

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	4	4	-3	-4	4	-	1	6	4	5	+	-8	10	0	1	12	2	-5	-11	0	4	7	-13

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Quadratic twists for elliptic curve 1558b1

-4	8	-3	5	-7	-19	41
12464c1	49856b1	14022k1	38950t1	76342c1	29602f1	63878b1

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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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