Cremona's table of elliptic curves

3045 = 3 · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	3045d	Isogeny class
Conductor	3045	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	10025708175 = 34 · 52 · 7 · 294	Discriminant
Eigenvalues	-1 3+ 5+ 7- -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1091,-13462]	[a1,a2,a3,a4,a6]
Generators	[-16:22:1]	Generators of the group modulo torsion
j	143622619359409/10025708175	j-invariant
L	1.6368900156563	L(r)(E,1)/r!
Ω	0.8343464995129	Real period
R	0.49047069071781	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48720cc3 9135m4 15225p3 21315x3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3045d3

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	+	+	-	-4	-2	2	4	-4	-	0	-2	2	8	0	6	-4	2	4	12	-10	-12	-12	10	14

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Quadratic twists for elliptic curve 3045d3

-4	-3	5	-7	29
48720cc3	9135m4	15225p3	21315x3	88305q3

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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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