Cremona's table of elliptic curves

10675 = 5² · 7 · 61

Field	Data	Notes
Atkin-Lehner	5- 7+ 61+	Signs for the Atkin-Lehner involutions
Class	10675m	Isogeny class
Conductor	10675	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	84000	Modular degree for the optimal curve
Δ	-5985163091796875 = -1 · 59 · 77 · 612	Discriminant
Eigenvalues	0  3 5- 7+  3  3 -5  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,22250,-3496094]	[a1,a2,a3,a4,a6]
j	623711453184/3064403503	j-invariant
L	3.4266217126098	L(r)(E,1)/r!
Ω	0.21416385703811	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	96075bw1 10675o1 74725s1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10675m1

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	3	-	+	3	3	-5	2	-4	-3	-4	6	0	12	3	2	6	+	4	16	-10	1	12	0	-3

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Quadratic twists for elliptic curve 10675m1

-3	5	-7
96075bw1	10675o1	74725s1

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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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