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	34656v	Isogeny class
Conductor	34656	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	569088	Modular degree for the optimal curve
Δ	-1732946251405839552 = -1 · 26 · 313 · 198	Discriminant
Eigenvalues	2- 3+  2 -1  0 -5 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-578442,180981828]	[a1,a2,a3,a4,a6]
j	-19692240832/1594323	j-invariant
L	0.51991525797966	L(r)(E,1)/r!
Ω	0.25995762899643	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	34656bb1 69312dc1 103968o1 34656q1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656v1

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	-1	0	-5	-6	+	0	-2	-9	-3	12	-9	-10	-12	14	-7	-1	12	5	-17	6	2	2

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Quadratic twists for elliptic curve 34656v1

-4	8	-3	-19
34656bb1	69312dc1	103968o1	34656q1

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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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