Cremona's table of elliptic curves

10082 = 2 · 71²

Field	Data	Notes
Atkin-Lehner	2+ 71-	Signs for the Atkin-Lehner involutions
Class	10082b	Isogeny class
Conductor	10082	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	184032	Modular degree for the optimal curve
Δ	366788005747592248 = 23 · 719	Discriminant
Eigenvalues	2+  1  0  3  6  3  6  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-708366,-227675928]	[a1,a2,a3,a4,a6]
j	857375/8	j-invariant
L	2.9638232070743	L(r)(E,1)/r!
Ω	0.16465684483746	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	80656n1 90738x1 10082c1	Quadratic twists by: -4 -3 -71

Hecke Eigenvalues for elliptic curve 10082b1

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
+	1	0	3	6	3	6	7	3	-6	9	2	0	-1	9	-6	6	6	-12	-	7	10	0	-3	12

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Quadratic twists for elliptic curve 10082b1

-4	-3	-71
80656n1	90738x1	10082c1

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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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