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	6	Product of Tamagawa factors cp
Δ	2312 = 23 · 172	Discriminant
Eigenvalues	2- -2  0 -4  6  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-43,105]	[a1,a2,a3,a4,a6]
j	8805624625/2312	j-invariant
L	0.74927722105228	L(r)(E,1)/r!
Ω	4.4956633263137	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	272d2 1088c2 306b2 850b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 34a2

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 34a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
272d2	1088c2	306b2	850b2	1666l2	4114b2	5746e2	578a2	12274d2	17986j2	28594f2	32674d2	46546a2	57154n2	62866c2	75106b2	95506a2	118354e2	126514e2

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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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