Cremona's table of elliptic curves

1288 = 2³ · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 7+ 23+	Signs for the Atkin-Lehner involutions
Class	1288a	Isogeny class
Conductor	1288	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	2308096 = 211 · 72 · 23	Discriminant
Eigenvalues	2+  0  2 7+  0 -4 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-979,11790]	[a1,a2,a3,a4,a6]
Generators	[22:30:1]	Generators of the group modulo torsion
j	50668941906/1127	j-invariant
L	2.7504832137211	L(r)(E,1)/r!
Ω	2.3936533408905	Real period
R	2.2981466586952	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	2576h2 10304a2 11592o2 32200w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1288a2

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

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Quadratic twists for elliptic curve 1288a2

-4	8	-3	5	-7	-23
2576h2	10304a2	11592o2	32200w2	9016a2	29624h2

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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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