Cremona's table of elliptic curves

53312 = 2⁶ · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 17+	Signs for the Atkin-Lehner involutions
Class	53312bs	Isogeny class
Conductor	53312	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	252435205624168448 = 219 · 78 · 174	Discriminant
Eigenvalues	2-  0  2 7-  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1657964,-821339568]	[a1,a2,a3,a4,a6]
Generators	[219730:5147744:125]	Generators of the group modulo torsion
j	16342588257633/8185058	j-invariant
L	6.2500001407987	L(r)(E,1)/r!
Ω	0.13305121215505	Real period
R	5.8717993240798	Regulator
r	1	Rank of the group of rational points
S	0.99999999999978	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53312n4 13328p3 7616i3	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 53312bs4

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

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Quadratic twists for elliptic curve 53312bs4

-4	8	-7
53312n4	13328p3	7616i3

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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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