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	3021b	Isogeny class
Conductor	3021	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-10646407060342731 = -1 · 32 · 19 · 538	Discriminant
Eigenvalues	-2 3-  1  3  5  2 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-285920,58959548]	[a1,a2,a3,a4,a6]
j	-2584989816536277323776/10646407060342731	j-invariant
L	1.6298229381596	L(r)(E,1)/r!
Ω	0.40745573453991	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	48336bb1 9063d1 75525c1 57399d1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3021b1

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	-	1	3	5	2	-5	+	4	6	2	8	0	-1	11	+	8	-1	-8	-12	-3	-8	-12	2	-2

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Quadratic twists for elliptic curve 3021b1

-4	-3	5	-19
48336bb1	9063d1	75525c1	57399d1

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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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