Cremona's table of elliptic curves

10309 = 13² · 61

Field	Data	Notes
Atkin-Lehner	13+ 61+	Signs for the Atkin-Lehner involutions
Class	10309c	Isogeny class
Conductor	10309	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3035334012841 = -1 · 138 · 612	Discriminant
Eigenvalues	-1  0 -2  4 -4 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1891,-89124]	[a1,a2,a3,a4,a6]
Generators	[196:2555:1]	Generators of the group modulo torsion
j	-154854153/628849	j-invariant
L	2.2263931430818	L(r)(E,1)/r!
Ω	0.33010114800491	Real period
R	3.3722893066835	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	92781h2 793a2	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 10309c2

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
-1	0	-2	4	-4	+	-6	2	-6	10	4	10	-2	-2	2	10	4	+	8	-12	6	-2	-10	-10	14

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Quadratic twists for elliptic curve 10309c2

-3	13
92781h2	793a2

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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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