Cremona's table of elliptic curves

21840 = 2⁴ · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7- 13+	Signs for the Atkin-Lehner involutions
Class	21840u	Isogeny class
Conductor	21840	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	319410000 = 24 · 33 · 54 · 7 · 132	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 13+ -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10655,-426900]	[a1,a2,a3,a4,a6]
j	8361897711794176/19963125	j-invariant
L	2.8194156570013	L(r)(E,1)/r!
Ω	0.46990260950023	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	10920e1 87360er1 65520u1 109200h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840u1

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
+	-	-	-	0	+	-6	0	-8	6	-4	6	-6	4	8	10	12	-10	-4	-12	-2	16	4	-6	14

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Quadratic twists for elliptic curve 21840u1

-4	8	-3	5
10920e1	87360er1	65520u1	109200h1

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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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