Cremona's table of elliptic curves

2288 = 2⁴ · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	2288a	Isogeny class
Conductor	2288	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	-843092966144 = -1 · 28 · 117 · 132	Discriminant
Eigenvalues	2+ -1 -1  2 11+ 13+  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2881,-73171]	[a1,a2,a3,a4,a6]
Generators	[172:2119:1]	Generators of the group modulo torsion
j	-10333900063744/3293331899	j-invariant
L	2.5878664205193	L(r)(E,1)/r!
Ω	0.32060161969238	Real period
R	4.0359534412246	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	1144d1 9152be1 20592h1 57200d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2288a1

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	-1	2	+	+	4	2	3	-6	-3	-3	-6	8	12	2	-13	-14	-13	7	12	-12	-12	-3	-17

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Quadratic twists for elliptic curve 2288a1

-4	8	-3	5	-7	-11	13
1144d1	9152be1	20592h1	57200d1	112112h1	25168g1	29744h1

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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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