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	3648bh	Isogeny class
Conductor	3648	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	8606711808 = 224 · 33 · 19	Discriminant
Eigenvalues	2- 3-  0  4  0  4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-513,-513]	[a1,a2,a3,a4,a6]
j	57066625/32832	j-invariant
L	3.2731413816312	L(r)(E,1)/r!
Ω	1.0910471272104	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	3648b1 912e1 10944ci1 91200gk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648bh1

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

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Quadratic twists for elliptic curve 3648bh1

-4	8	-3	5	-19
3648b1	912e1	10944ci1	91200gk1	69312cm1

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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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