Cremona's table of elliptic curves

10815 = 3 · 5 · 7 · 103

Field	Data	Notes
Atkin-Lehner	3- 5- 7- 103-	Signs for the Atkin-Lehner involutions
Class	10815l	Isogeny class
Conductor	10815	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	1460025 = 34 · 52 · 7 · 103	Discriminant
Eigenvalues	-1 3- 5- 7- -2  0 -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1215,16200]	[a1,a2,a3,a4,a6]
Generators	[15:30:1]	Generators of the group modulo torsion
j	198369494210161/1460025	j-invariant
L	3.7149251337867	L(r)(E,1)/r!
Ω	2.4101629172518	Real period
R	0.77067925723932	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	32445l1 54075e1 75705c1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10815l1

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	-	-	-	-2	0	-4	6	-8	-6	4	4	-2	8	-8	12	-14	-2	8	2	2	-8	-12	2	-12

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Quadratic twists for elliptic curve 10815l1

-3	5	-7
32445l1	54075e1	75705c1

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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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