Cremona's table of elliptic curves

10318 = 2 · 7 · 11 · 67

Field	Data	Notes
Atkin-Lehner	2- 7+ 11+ 67-	Signs for the Atkin-Lehner involutions
Class	10318g	Isogeny class
Conductor	10318	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	2800	Modular degree for the optimal curve
Δ	-165088 = -1 · 25 · 7 · 11 · 67	Discriminant
Eigenvalues	2-  0 -4 7+ 11+ -3  7  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-82,305]	[a1,a2,a3,a4,a6]
Generators	[5:-1:1]	Generators of the group modulo torsion
j	-60282398961/165088	j-invariant
L	4.5514522656803	L(r)(E,1)/r!
Ω	3.2371458846154	Real period
R	0.28120155395598	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	82544bf1 92862r1 72226j1 113498i1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 10318g1

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	+	+	-3	7	2	5	9	-8	2	-4	-12	6	9	4	-11	-	-5	5	-9	-8	2	19

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Quadratic twists for elliptic curve 10318g1

-4	-3	-7	-11
82544bf1	92862r1	72226j1	113498i1

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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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