Cremona's table of elliptic curves

34080 = 2⁵ · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 71-	Signs for the Atkin-Lehner involutions
Class	34080f	Isogeny class
Conductor	34080	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	116144640 = 29 · 32 · 5 · 712	Discriminant
Eigenvalues	2+ 3+ 5+  2 -2 -6 -8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-456,-3564]	[a1,a2,a3,a4,a6]
Generators	[-12:6:1] [53:344:1]	Generators of the group modulo torsion
j	20525811272/226845	j-invariant
L	7.3291133164926	L(r)(E,1)/r!
Ω	1.0336393250929	Real period
R	3.5452953165424	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34080q2 68160dn2 102240bh2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 34080f2

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

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Quadratic twists for elliptic curve 34080f2

-4	8	-3
34080q2	68160dn2	102240bh2

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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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