Cremona's table of elliptic curves

10032 = 2⁴ · 3 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 19-	Signs for the Atkin-Lehner involutions
Class	10032a	Isogeny class
Conductor	10032	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	68544	Modular degree for the optimal curve
Δ	-49544922067483392 = -1 · 28 · 39 · 11 · 197	Discriminant
Eigenvalues	2+ 3+  0 -2 11+  7  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,53647,9564093]	[a1,a2,a3,a4,a6]
j	66697871337344000/193534851826107	j-invariant
L	1.7569125964699	L(r)(E,1)/r!
Ω	0.25098751378141	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5016e1 40128bx1 30096i1 110352e1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10032a1

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	+	7	5	-	2	8	0	-2	2	-4	6	-1	1	10	2	3	8	3	11	-11	-2

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Quadratic twists for elliptic curve 10032a1

-4	8	-3	-11
5016e1	40128bx1	30096i1	110352e1

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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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