Cremona's table of elliptic curves

127680 = 2⁶ · 3 · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	127680ct	Isogeny class
Conductor	127680	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	1320476774400 = 212 · 36 · 52 · 72 · 192	Discriminant
Eigenvalues	2+ 3- 5- 7+  4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-23945,1417143]	[a1,a2,a3,a4,a6]
Generators	[31:840:1]	Generators of the group modulo torsion
j	370703277125056/322382025	j-invariant
L	9.0893402196452	L(r)(E,1)/r!
Ω	0.85241735966412	Real period
R	0.88858469019702	Regulator
r	1	Rank of the group of rational points
S	1.0000000037601	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	127680bt2 63840b1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 127680ct2

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

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Quadratic twists for elliptic curve 127680ct2

-4	8
127680bt2	63840b1

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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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