Cremona's table of elliptic curves

88 = 2³ · 11

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	88a	Isogeny class
Conductor	88	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-2816 = -1 · 28 · 11	Discriminant
Eigenvalues	2+ -3 -3 -2 11+  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4,4]	[a1,a2,a3,a4,a6]
Generators	[2:-2:1]	Generators of the group modulo torsion
j	-27648/11	j-invariant
L	0.68490159390412	L(r)(E,1)/r!
Ω	4.2525295331484	Real period
R	0.040264364336881	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	176a1 704e1 792f1 2200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 88a1

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
+	-3	-3	-2	+	0	-6	4	1	-8	-7	-1	4	6	-8	2	-1	4	-5	3	16	2	-2	15	-7

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Quadratic twists for elliptic curve 88a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
176a1	704e1	792f1	2200g1	4312f1	968e1	14872j1	25432o1	31768h1	46552g1	74008i1	84568h1	120472h1

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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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