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	1824d	Isogeny class
Conductor	1824	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-184327778304 = -1 · 212 · 38 · 193	Discriminant
Eigenvalues	2+ 3- -1 -1 -5  4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1501,29963]	[a1,a2,a3,a4,a6]
Generators	[-19:228:1]	Generators of the group modulo torsion
j	-91368216064/45001899	j-invariant
L	3.15882296728	L(r)(E,1)/r!
Ω	0.94257927516903	Real period
R	0.069817800530924	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	1824e1 3648c1 5472u1 45600bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824d1

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 1824d1

-4	8	-3	5	-7	-19
1824e1	3648c1	5472u1	45600bc1	89376f1	34656w1

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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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