Cremona's table of elliptic curves

10230 = 2 · 3 · 5 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11+ 31-	Signs for the Atkin-Lehner involutions
Class	10230bd	Isogeny class
Conductor	10230	Conductor
∏ cp	1536	Product of Tamagawa factors cp
deg	147456	Modular degree for the optimal curve
Δ	-546008548073472000 = -1 · 216 · 38 · 53 · 11 · 314	Discriminant
Eigenvalues	2- 3- 5-  0 11+ -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,105940,-32972400]	[a1,a2,a3,a4,a6]
Generators	[280:4180:1]	Generators of the group modulo torsion
j	131493220370352740159/546008548073472000	j-invariant
L	8.1943535879424	L(r)(E,1)/r!
Ω	0.14785000418735	Real period
R	0.57732734160925	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	81840ce1 30690i1 51150a1 112530be1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10230bd1

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

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Quadratic twists for elliptic curve 10230bd1

-4	-3	5	-11
81840ce1	30690i1	51150a1	112530be1

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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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