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	1288g	Isogeny class
Conductor	1288	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-1122245340272 = -1 · 24 · 78 · 233	Discriminant
Eigenvalues	2-  3  2 7+  2 -1  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8419,301667]	[a1,a2,a3,a4,a6]
j	-4124632486295808/70140333767	j-invariant
L	3.4849926874943	L(r)(E,1)/r!
Ω	0.87124817187357	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2576i1 10304b1 11592d1 32200k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1288g1

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	2	+	2	-1	0	2	+	-3	-1	-2	-1	8	-5	-6	0	6	-10	7	13	-2	-4	-12	-12

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Quadratic twists for elliptic curve 1288g1

-4	8	-3	5	-7	-23
2576i1	10304b1	11592d1	32200k1	9016l1	29624p1

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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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