Cremona's table of elliptic curves

79296 = 2⁶ · 3 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 59+	Signs for the Atkin-Lehner involutions
Class	79296w	Isogeny class
Conductor	79296	Conductor
∏ cp	352	Product of Tamagawa factors cp
deg	2703360	Modular degree for the optimal curve
Δ	3948662945354416128 = 216 · 311 · 78 · 59	Discriminant
Eigenvalues	2+ 3-  0 7- -4  0  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13909953,19963228959]	[a1,a2,a3,a4,a6]
Generators	[1923:18144:1]	Generators of the group modulo torsion
j	4541724645902232578500/60251814962073	j-invariant
L	8.4521800820747	L(r)(E,1)/r!
Ω	0.22567254766513	Real period
R	0.42560560381277	Regulator
r	1	Rank of the group of rational points
S	1.0000000002049	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	79296bh1 9912d1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 79296w1

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	6	4	-4	0	2	4	-2	8	-4	4	+	4	-4	2	2	-16	12	-6	-18

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Quadratic twists for elliptic curve 79296w1

-4	8
79296bh1	9912d1

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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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