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	10318a	Isogeny class
Conductor	10318	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	20480	Modular degree for the optimal curve
Δ	-2337034594048 = -1 · 28 · 75 · 112 · 672	Discriminant
Eigenvalues	2+  2  0 7+ 11+ -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3580,109008]	[a1,a2,a3,a4,a6]
Generators	[27:168:1]	Generators of the group modulo torsion
j	-5076475881639625/2337034594048	j-invariant
L	4.4071643295271	L(r)(E,1)/r!
Ω	0.7644536357175	Real period
R	2.8825582897455	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82544bl1 92862bo1 72226a1 113498v1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 10318a1

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	0	+	+	-2	0	2	8	-6	-10	10	2	12	8	-2	0	10	+	-8	-8	-16	2	-6	-8

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Quadratic twists for elliptic curve 10318a1

-4	-3	-7	-11
82544bl1	92862bo1	72226a1	113498v1

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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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