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	3045b	Isogeny class
Conductor	3045	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1872	Modular degree for the optimal curve
Δ	-139847715 = -1 · 39 · 5 · 72 · 29	Discriminant
Eigenvalues	2 3+ 5+ 7- -3  4  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-36,587]	[a1,a2,a3,a4,a6]
j	-5304438784/139847715	j-invariant
L	3.0800474183932	L(r)(E,1)/r!
Ω	1.5400237091966	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48720bz1 9135o1 15225m1 21315s1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3045b1

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
2	+	+	-	-3	4	6	0	5	+	-10	7	-7	11	12	7	6	-4	12	8	-9	10	9	6	-7

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Quadratic twists for elliptic curve 3045b1

-4	-3	5	-7	29
48720bz1	9135o1	15225m1	21315s1	88305s1

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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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