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	10230w	Isogeny class
Conductor	10230	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	612889243560000 = 26 · 32 · 54 · 116 · 312	Discriminant
Eigenvalues	2- 3+ 5+  0 11+ -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-330101,-73127077]	[a1,a2,a3,a4,a6]
Generators	[787:12068:1]	Generators of the group modulo torsion
j	3977995745205517092049/612889243560000	j-invariant
L	5.2333381997666	L(r)(E,1)/r!
Ω	0.19917822277075	Real period
R	4.3791084244102	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	81840cw2 30690q2 51150w2 112530i2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 10230w2

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

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Quadratic twists for elliptic curve 10230w2

-4	-3	5	-11
81840cw2	30690q2	51150w2	112530i2

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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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