Cremona's table of elliptic curves

34680 = 2³ · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 17+	Signs for the Atkin-Lehner involutions
Class	34680ba	Isogeny class
Conductor	34680	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	-530604000000 = -1 · 28 · 33 · 56 · 173	Discriminant
Eigenvalues	2+ 3- 5- -4 -4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,1740,-20592]	[a1,a2,a3,a4,a6]
Generators	[36:300:1]	Generators of the group modulo torsion
j	462951088/421875	j-invariant
L	5.5486724535403	L(r)(E,1)/r!
Ω	0.50758538228071	Real period
R	0.60730586717679	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69360u2 104040cm2 34680d2	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 34680ba2

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

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Quadratic twists for elliptic curve 34680ba2

-4	-3	17
69360u2	104040cm2	34680d2

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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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