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	34656p	Isogeny class
Conductor	34656	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	218880	Modular degree for the optimal curve
Δ	-1177164721497792 = -1 · 26 · 3 · 1910	Discriminant
Eigenvalues	2+ 3-  2 -1  0 -3  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-304082,64460628]	[a1,a2,a3,a4,a6]
Generators	[18984:380638:27]	Generators of the group modulo torsion
j	-7924672/3	j-invariant
L	7.8631074022687	L(r)(E,1)/r!
Ω	0.4784613066658	Real period
R	8.2170776327387	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34656g1 69312cr1 103968cd1 34656u1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656p1

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	-3	2	-	8	-6	-7	11	4	-1	6	-12	-6	1	-7	-4	-11	1	-2	-10	14

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Quadratic twists for elliptic curve 34656p1

-4	8	-3	-19
34656g1	69312cr1	103968cd1	34656u1

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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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