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	10230z	Isogeny class
Conductor	10230	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	20480	Modular degree for the optimal curve
Δ	1298964480000 = 216 · 3 · 54 · 11 · 312	Discriminant
Eigenvalues	2- 3+ 5- -2 11+  0 -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3075,34785]	[a1,a2,a3,a4,a6]
Generators	[3:158:1]	Generators of the group modulo torsion
j	3215643533722801/1298964480000	j-invariant
L	5.6785091540729	L(r)(E,1)/r!
Ω	0.7797093634589	Real period
R	0.22758917537885	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	81840do1 30690h1 51150s1 112530o1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10230z1

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
-	+	-	-2	+	0	-6	6	4	-6	+	-10	6	8	-6	8	10	0	-16	-6	4	4	-12	-12	-2

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Quadratic twists for elliptic curve 10230z1

-4	-3	5	-11
81840do1	30690h1	51150s1	112530o1

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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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