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	34656s	Isogeny class
Conductor	34656	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-3260844103872 = -1 · 26 · 3 · 198	Discriminant
Eigenvalues	2+ 3-  2 -4  6  2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-842,87108]	[a1,a2,a3,a4,a6]
Generators	[498:7550:27]	Generators of the group modulo torsion
j	-21952/1083	j-invariant
L	8.0573739958829	L(r)(E,1)/r!
Ω	0.65978182181136	Real period
R	6.1060897174788	Regulator
r	1	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34656i1 69312cu2 103968ci1 1824f1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656s1

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

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Quadratic twists for elliptic curve 34656s1

-4	8	-3	-19
34656i1	69312cu2	103968ci1	1824f1

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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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