Cremona's table of elliptic curves

215 = 5 · 43

Field	Data	Notes
Atkin-Lehner	5+ 43+	Signs for the Atkin-Lehner involutions
Class	215a	Isogeny class
Conductor	215	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-26875 = -1 · 54 · 43	Discriminant
Eigenvalues	0  0 5+ -2 -1 -1 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-8,-12]	[a1,a2,a3,a4,a6]
Generators	[6:12:1]	Generators of the group modulo torsion
j	-56623104/26875	j-invariant
L	1.213693422283	L(r)(E,1)/r!
Ω	1.3878357095558	Real period
R	0.4372612024342	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	3440d1 13760j1 1935j1 1075a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 215a1

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	0	+	-2	-1	-1	-3	-2	-1	4	3	-8	5	+	0	-5	12	-4	-3	6	-8	0	-9	-6	-17

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Quadratic twists for elliptic curve 215a1

-4	8	-3	5	-7	-11	13	17	-19	-23	-43
3440d1	13760j1	1935j1	1075a1	10535c1	26015d1	36335c1	62135b1	77615a1	113735i1	9245c1

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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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