Cremona's table of elliptic curves

15008 = 2⁵ · 7 · 67

Field	Data	Notes
Atkin-Lehner	2+ 7+ 67+	Signs for the Atkin-Lehner involutions
Class	15008a	Isogeny class
Conductor	15008	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	134741824 = 26 · 7 · 673	Discriminant
Eigenvalues	2+  1 -3 7+  2 -1 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-362,-2716]	[a1,a2,a3,a4,a6]
Generators	[-10:2:1]	Generators of the group modulo torsion
j	82199392192/2105341	j-invariant
L	4.1081127617552	L(r)(E,1)/r!
Ω	1.0959758369365	Real period
R	1.8741803529348	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	15008h1 30016bp1 105056a1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 15008a1

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	-3	+	2	-1	-2	0	-1	-1	5	7	5	4	4	4	-8	10	+	15	-12	8	-16	12	-14

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Quadratic twists for elliptic curve 15008a1

-4	8	-7
15008h1	30016bp1	105056a1

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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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