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	3648g	Isogeny class
Conductor	3648	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	14942208 = 218 · 3 · 19	Discriminant
Eigenvalues	2+ 3+  2  0  0 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-97,-287]	[a1,a2,a3,a4,a6]
j	389017/57	j-invariant
L	1.5348491927153	L(r)(E,1)/r!
Ω	1.5348491927153	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	3648bf1 57b2 10944bh1 91200dn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648g1

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

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Quadratic twists for elliptic curve 3648g1

-4	8	-3	5	-19
3648bf1	57b2	10944bh1	91200dn1	69312br1

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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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