Cremona's table of elliptic curves

3648 = 2⁶ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 19+	Signs for the Atkin-Lehner involutions
Class	3648c	Isogeny class
Conductor	3648	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-2880121536 = -1 · 26 · 38 · 193	Discriminant
Eigenvalues	2+ 3+  1 -1  5 -4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-375,3933]	[a1,a2,a3,a4,a6]
Generators	[-12:81:1]	Generators of the group modulo torsion
j	-91368216064/45001899	j-invariant
L	3.1910913156024	L(r)(E,1)/r!
Ω	1.3330083945559	Real period
R	1.1969509451835	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3648p1 1824d1 10944r1 91200cr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648c1

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	-1	5	-4	-3	+	0	4	-2	-4	-4	5	-7	2	10	-15	14	2	-3	-14	0	10	4

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Quadratic twists for elliptic curve 3648c1

-4	8	-3	5	-19
3648p1	1824d1	10944r1	91200cr1	69312bp1

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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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