Cremona's table of elliptic curves

21648 = 2⁴ · 3 · 11 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 41+	Signs for the Atkin-Lehner involutions
Class	21648s	Isogeny class
Conductor	21648	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	248832	Modular degree for the optimal curve
Δ	390797305810255872 = 230 · 39 · 11 · 412	Discriminant
Eigenvalues	2- 3+  0  2 11- -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-184128,-4432896]	[a1,a2,a3,a4,a6]
Generators	[-48741280:-88772608:117649]	Generators of the group modulo torsion
j	168548786637666625/95409498488832	j-invariant
L	4.7921571444032	L(r)(E,1)/r!
Ω	0.24857249871955	Real period
R	9.6393550555444	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	2706o1 86592cr1 64944be1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 21648s1

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

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Quadratic twists for elliptic curve 21648s1

-4	8	-3
2706o1	86592cr1	64944be1

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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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