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	35192575602 = 2 · 36 · 176	Discriminant
Eigenvalues	2+ 3-  0 -4 -6  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1017,8883]	[a1,a2,a3,a4,a6]
Generators	[7:42:1]	Generators of the group modulo torsion
j	159661140625/48275138	j-invariant
L	1.2110949195557	L(r)(E,1)/r!
Ω	1.0762819712483	Real period
R	3.3757740589608	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	2448q4 9792v4 34a4 7650by4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 306b4

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 306b4

-4	8	-3	5	-7	-11	13	17	-19
2448q4	9792v4	34a4	7650by4	14994t4	37026ba4	51714s4	5202a4	110466bp4

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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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