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	34680m	Isogeny class
Conductor	34680	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	587520	Modular degree for the optimal curve
Δ	580606243329312000 = 28 · 32 · 53 · 1710	Discriminant
Eigenvalues	2+ 3+ 5-  4 -1  4 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2115865,-1183350275]	[a1,a2,a3,a4,a6]
j	2029825024/1125	j-invariant
L	3.0043687621376	L(r)(E,1)/r!
Ω	0.1251820317552	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	69360bv1 104040ci1 34680w1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 34680m1

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	-1	4	+	-1	2	1	0	-2	5	2	6	-2	-1	-5	-12	3	-4	11	10	11	6

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Quadratic twists for elliptic curve 34680m1

-4	-3	17
69360bv1	104040ci1	34680w1

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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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