Cremona's table of elliptic curves

34656 = 2⁵ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19-	Signs for the Atkin-Lehner involutions
Class	34656x	Isogeny class
Conductor	34656	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	578099785728 = 212 · 3 · 196	Discriminant
Eigenvalues	2- 3+  2 -4  4  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6257,189057]	[a1,a2,a3,a4,a6]
Generators	[33:132:1]	Generators of the group modulo torsion
j	140608/3	j-invariant
L	4.7839691257857	L(r)(E,1)/r!
Ω	0.91865160759423	Real period
R	2.6037994633864	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	34656r3 69312bv1 103968z3 96a2	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656x3

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	-4	4	2	-6	-	0	-2	-4	2	-2	4	8	-10	4	6	-4	16	-6	-4	12	-10	14

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Quadratic twists for elliptic curve 34656x3

-4	8	-3	-19
34656r3	69312bv1	103968z3	96a2

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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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