Cremona's table of elliptic curves

90738 = 2 · 3² · 71²

Field	Data	Notes
Atkin-Lehner	2- 3+ 71-	Signs for the Atkin-Lehner involutions
Class	90738w	Isogeny class
Conductor	90738	Conductor
∏ cp	82	Product of Tamagawa factors cp
deg	1535040	Modular degree for the optimal curve
Δ	-299302458243416064 = -1 · 241 · 33 · 712	Discriminant
Eigenvalues	2- 3+  2 -5  4  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,163171,6974373]	[a1,a2,a3,a4,a6]
Generators	[47:3816:1]	Generators of the group modulo torsion
j	3529999721882781/2199023255552	j-invariant
L	10.707832421899	L(r)(E,1)/r!
Ω	0.19011107165381	Real period
R	0.6868791024179	Regulator
r	1	Rank of the group of rational points
S	0.99999999970139	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	90738f1 90738v1	Quadratic twists by: -3 -71

Hecke Eigenvalues for elliptic curve 90738w1

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	-5	4	0	0	-4	2	-3	5	6	12	2	-6	-9	-7	-6	14	-	-11	-5	5	-18	-6

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Quadratic twists for elliptic curve 90738w1

-3	-71
90738f1	90738v1

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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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