Cremona's table of elliptic curves

75712 = 2⁶ · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	75712u	Isogeny class
Conductor	75712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	179712	Modular degree for the optimal curve
Δ	-232789970236096 = -1 · 26 · 73 · 139	Discriminant
Eigenvalues	2+  0 -3 7+ -2 13-  2  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4394,-742586]	[a1,a2,a3,a4,a6]
j	-13824/343	j-invariant
L	0.48306893405993	L(r)(E,1)/r!
Ω	0.24153445600012	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	75712bo1 37856m1 75712bn1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712u1

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	-3	+	-2	-	2	3	-3	1	9	-6	-6	-9	-1	5	4	6	4	-10	-3	-3	1	9	-15

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Quadratic twists for elliptic curve 75712u1

-4	8	13
75712bo1	37856m1	75712bn1

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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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