Cremona's table of elliptic curves

4488 = 2³ · 3 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 17+	Signs for the Atkin-Lehner involutions
Class	4488a	Isogeny class
Conductor	4488	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3071084544 = 211 · 36 · 112 · 17	Discriminant
Eigenvalues	2+ 3+ -2 -2 11+  0 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-824,-8436]	[a1,a2,a3,a4,a6]
Generators	[-15:18:1]	Generators of the group modulo torsion
j	30248395634/1499553	j-invariant
L	2.5086457014957	L(r)(E,1)/r!
Ω	0.89373384048604	Real period
R	2.8069270602213	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	8976j2 35904bj2 13464u2 112200cd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4488a2

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

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Quadratic twists for elliptic curve 4488a2

-4	8	-3	5	-11	17
8976j2	35904bj2	13464u2	112200cd2	49368z2	76296h2

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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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