Cremona's table of elliptic curves

10388 = 2² · 7² · 53

Field	Data	Notes
Atkin-Lehner	2- 7- 53+	Signs for the Atkin-Lehner involutions
Class	10388f	Isogeny class
Conductor	10388	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	69673274939715328 = 28 · 713 · 532	Discriminant
Eigenvalues	2-  0  4 7-  0  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-215220103,-1215268849410]	[a1,a2,a3,a4,a6]
Generators	[-7493595010442094147153760956587685:6856846668293553942510796323762:884725655541116555703406551625]	Generators of the group modulo torsion
j	36605303452610058192336/2313332287	j-invariant
L	5.5614022133957	L(r)(E,1)/r!
Ω	0.039416571483226	Real period
R	47.03099909609	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	41552bc2 93492bd2 1484b2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 10388f2

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

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Quadratic twists for elliptic curve 10388f2

-4	-3	-7
41552bc2	93492bd2	1484b2

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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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