Cremona's table of elliptic curves

306 = 2 · 3² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 17-	Signs for the Atkin-Lehner involutions
Class	306b	Isogeny class
Conductor	306	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	14326308 = 22 · 36 · 173	Discriminant
Eigenvalues	2+ 3-  0 -4 -6  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-927,11097]	[a1,a2,a3,a4,a6]
Generators	[-32:101:1]	Generators of the group modulo torsion
j	120920208625/19652	j-invariant
L	1.2110949195557	L(r)(E,1)/r!
Ω	2.1525639424966	Real period
R	1.6878870294804	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	2448q3 9792v3 34a3 7650by3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 306b3

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
+	-	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 306b3

-4	8	-3	5	-7	-11	13	17	-19
2448q3	9792v3	34a3	7650by3	14994t3	37026ba3	51714s3	5202a3	110466bp3

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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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