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	53312bw	Isogeny class
Conductor	53312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8192135168 = 212 · 76 · 17	Discriminant
Eigenvalues	2- -2  2 7- -2  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4377,109927]	[a1,a2,a3,a4,a6]
Generators	[-61:392:1]	Generators of the group modulo torsion
j	19248832/17	j-invariant
L	4.3010451259472	L(r)(E,1)/r!
Ω	1.3021911353217	Real period
R	1.651464600439	Regulator
r	1	Rank of the group of rational points
S	0.99999999999275	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53312bu2 26656b1 1088l2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 53312bw2

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
-	-2	2	-	-2	2	+	4	-2	-2	-10	-10	-2	-4	0	-6	4	2	16	10	6	6	-4	-6	14

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Quadratic twists for elliptic curve 53312bw2

-4	8	-7
53312bu2	26656b1	1088l2

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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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