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	1824a	Isogeny class
Conductor	1824	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1663488 = -1 · 29 · 32 · 192	Discriminant
Eigenvalues	2+ 3+  0  0  0  0 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,-60]	[a1,a2,a3,a4,a6]
Generators	[8:18:1]	Generators of the group modulo torsion
j	-125000/3249	j-invariant
L	2.5529043229522	L(r)(E,1)/r!
Ω	1.1539823467741	Real period
R	1.1061279793789	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1824j2 3648o2 5472r2 45600bn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824a2

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

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Quadratic twists for elliptic curve 1824a2

-4	8	-3	5	-7	-19
1824j2	3648o2	5472r2	45600bn2	89376v2	34656bd2

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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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