Cremona's table of elliptic curves

8184 = 2³ · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 31-	Signs for the Atkin-Lehner involutions
Class	8184h	Isogeny class
Conductor	8184	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	305865899615232 = 210 · 35 · 113 · 314	Discriminant
Eigenvalues	2+ 3-  0 -2 11+  0  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-105248,13080240]	[a1,a2,a3,a4,a6]
Generators	[-68:4464:1]	Generators of the group modulo torsion
j	125912671148474500/298697167593	j-invariant
L	4.8358460927455	L(r)(E,1)/r!
Ω	0.5463793098423	Real period
R	0.8850712326829	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	16368b1 65472j1 24552v1 90024bd1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8184h1

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

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Quadratic twists for elliptic curve 8184h1

-4	8	-3	-11
16368b1	65472j1	24552v1	90024bd1

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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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