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	306d	Isogeny class
Conductor	306	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	446148 = 22 · 38 · 17	Discriminant
Eigenvalues	2- 3-  4 -2  0 -6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-23,-21]	[a1,a2,a3,a4,a6]
j	1771561/612	j-invariant
L	2.2491921793764	L(r)(E,1)/r!
Ω	2.2491921793764	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	2448t1 9792bb1 102a1 7650o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 306d1

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
-	-	4	-2	0	-6	-	4	-6	4	-6	-4	10	-4	-4	2	-12	-4	-12	6	2	10	12	2	6

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Quadratic twists for elliptic curve 306d1

-4	8	-3	5	-7	-11	13	17	-19
2448t1	9792bb1	102a1	7650o1	14994cs1	37026p1	51714k1	5202l1	110466w1

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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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