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	34656k	Isogeny class
Conductor	34656	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	276480	Modular degree for the optimal curve
Δ	-296565190078464 = -1 · 212 · 34 · 197	Discriminant
Eigenvalues	2+ 3+  3  3  3  0  1 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-414909,103009077]	[a1,a2,a3,a4,a6]
j	-40992251392/1539	j-invariant
L	4.0950606606903	L(r)(E,1)/r!
Ω	0.51188258258653	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	34656bg1 69312bx1 103968cj1 1824l1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656k1

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
+	+	3	3	3	0	1	-	0	8	2	4	12	-1	9	-6	6	-1	10	10	-11	-6	0	6	8

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Quadratic twists for elliptic curve 34656k1

-4	8	-3	-19
34656bg1	69312bx1	103968cj1	1824l1

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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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