Cremona's table of elliptic curves

309 = 3 · 103

Field	Data	Notes
Atkin-Lehner	3- 103-	Signs for the Atkin-Lehner involutions
Class	309a	Isogeny class
Conductor	309	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	-25029 = -1 · 35 · 103	Discriminant
Eigenvalues	-1 3- -1 -2 -2 -5  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6,9]	[a1,a2,a3,a4,a6]
Generators	[3:-6:1]	Generators of the group modulo torsion
j	-24137569/25029	j-invariant
L	1.2276894796603	L(r)(E,1)/r!
Ω	3.4344206939524	Real period
R	0.071493249608129	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4944d1 19776f1 927a1 7725a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 309a1

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
-1	-	-1	-2	-2	-5	0	-8	1	-2	5	2	8	-11	-2	10	-11	-5	11	16	12	6	1	-6	-7

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Quadratic twists for elliptic curve 309a1

-4	8	-3	5	-7	-11	13	17	-19	-103
4944d1	19776f1	927a1	7725a1	15141c1	37389d1	52221g1	89301a1	111549a1	31827a1

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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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