Cremona's table of elliptic curves

3021 = 3 · 19 · 53

Field	Data	Notes
Atkin-Lehner	3- 19+ 53+	Signs for the Atkin-Lehner involutions
Class	3021a	Isogeny class
Conductor	3021	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	12969153 = 35 · 19 · 532	Discriminant
Eigenvalues	1 3-  4  0  2  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-79,-211]	[a1,a2,a3,a4,a6]
j	53540005609/12969153	j-invariant
L	4.0802281321664	L(r)(E,1)/r!
Ω	1.6320912528666	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	48336bd1 9063c1 75525b1 57399c1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3021a1

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	0	2	2	-2	+	4	6	-4	2	-6	-4	2	+	8	14	4	0	-6	16	0	-10	-2

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Quadratic twists for elliptic curve 3021a1

-4	-3	5	-19
48336bd1	9063c1	75525b1	57399c1

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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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