Cremona's table of elliptic curves

1824 = 2⁵ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 19-	Signs for the Atkin-Lehner involutions
Class	1824c	Isogeny class
Conductor	1824	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	1871424 = 26 · 34 · 192	Discriminant
Eigenvalues	2+ 3+ -2  4 -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-114,504]	[a1,a2,a3,a4,a6]
j	2582630848/29241	j-invariant
L	1.3231098750361	L(r)(E,1)/r!
Ω	2.6462197500721	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1824i1 3648l2 5472v1 45600bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824c1

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

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Quadratic twists for elliptic curve 1824c1

-4	8	-3	5	-7	-19
1824i1	3648l2	5472v1	45600bw1	89376t1	34656bf1

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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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