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	21840d	Isogeny class
Conductor	21840	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	515970000 = 24 · 34 · 54 · 72 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-132711,-18564210]	[a1,a2,a3,a4,a6]
Generators	[11658:56924:27]	Generators of the group modulo torsion
j	16155773913566746624/32248125	j-invariant
L	3.8463092013279	L(r)(E,1)/r!
Ω	0.25013389831831	Real period
R	7.68850049351	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	10920p1 87360hb1 65520bp1 109200bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840d1

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

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Quadratic twists for elliptic curve 21840d1

-4	8	-3	5
10920p1	87360hb1	65520bp1	109200bm1

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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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