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	53312bn	Isogeny class
Conductor	53312	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-668745728 = -1 · 214 · 74 · 17	Discriminant
Eigenvalues	2- -3 -4 7+  1 -3 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1372,19600]	[a1,a2,a3,a4,a6]
Generators	[28:-56:1] [22:8:1]	Generators of the group modulo torsion
j	-7260624/17	j-invariant
L	4.4645794113485	L(r)(E,1)/r!
Ω	1.6186132158464	Real period
R	0.22985620075062	Regulator
r	2	Rank of the group of rational points
S	0.99999999999957	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53312h1 13328k1 53312cm1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 53312bn1

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	-4	+	1	-3	+	-2	-4	0	-8	-8	0	10	10	-3	-14	8	-10	5	-16	-11	12	9	10

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Quadratic twists for elliptic curve 53312bn1

-4	8	-7
53312h1	13328k1	53312cm1

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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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