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	10032b	Isogeny class
Conductor	10032	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	12198912 = 210 · 3 · 11 · 192	Discriminant
Eigenvalues	2+ 3+  0  2 11- -4  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3968,-94896]	[a1,a2,a3,a4,a6]
Generators	[85:418:1]	Generators of the group modulo torsion
j	6749136170500/11913	j-invariant
L	3.9987303392832	L(r)(E,1)/r!
Ω	0.60151652713339	Real period
R	3.3238740407847	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	5016c1 40128bq1 30096d1 110352f1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10032b1

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	-	-4	2	-	-6	6	4	2	6	0	-10	-4	-8	4	-4	6	10	-14	4	-14	-2

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Quadratic twists for elliptic curve 10032b1

-4	8	-3	-11
5016c1	40128bq1	30096d1	110352f1

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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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