Cremona's table of elliptic curves

15015 = 3 · 5 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	15015v	Isogeny class
Conductor	15015	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	-695269575 = -1 · 34 · 52 · 74 · 11 · 13	Discriminant
Eigenvalues	1 3- 5- 7+ 11- 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-73,-1297]	[a1,a2,a3,a4,a6]
j	-42180533641/695269575	j-invariant
L	2.7650734831995	L(r)(E,1)/r!
Ω	0.69126837079988	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45045m1 75075w1 105105t1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 15015v1

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	-	-	+	-	+	-6	-4	8	2	8	-10	6	-4	12	-2	0	-14	-8	16	-10	-8	12	-14	-10

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Quadratic twists for elliptic curve 15015v1

-3	5	-7
45045m1	75075w1	105105t1

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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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