Cremona's table of elliptic curves

34 = 2 · 17

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	34a	Isogeny class
Conductor	34	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	48275138 = 2 · 176	Discriminant
Eigenvalues	2- -2  0 -4  6  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-113,-329]	[a1,a2,a3,a4,a6]
j	159661140625/48275138	j-invariant
L	0.74927722105228	L(r)(E,1)/r!
Ω	1.4985544421046	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	272d4 1088c4 306b4 850b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 34a4

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	0	-4	6	2	+	-4	0	0	-4	-4	6	8	0	-6	0	-4	8	0	2	8	0	-6	14

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Quadratic twists for elliptic curve 34a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
272d4	1088c4	306b4	850b4	1666l4	4114b4	5746e4	578a4	12274d4	17986j4	28594f4	32674d4	46546a4	57154n4	62866c4	75106b4	95506a4	118354e4	126514e4

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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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