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	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	3648 = 26 · 3 · 19	Discriminant
Eigenvalues	2+ 3+  0  0  0  0 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18,-24]	[a1,a2,a3,a4,a6]
Generators	[7:12:1]	Generators of the group modulo torsion
j	10648000/57	j-invariant
L	2.5529043229522	L(r)(E,1)/r!
Ω	2.3079646935482	Real period
R	2.2122559587577	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	1824j1 3648o1 5472r1 45600bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1824a1

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 1824a1

-4	8	-3	5	-7	-19
1824j1	3648o1	5472r1	45600bn1	89376v1	34656bd1

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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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