Cremona's table of elliptic curves

10248 = 2³ · 3 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 61-	Signs for the Atkin-Lehner involutions
Class	10248g	Isogeny class
Conductor	10248	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	3873744 = 24 · 34 · 72 · 61	Discriminant
Eigenvalues	2- 3- -2 7-  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-999,11826]	[a1,a2,a3,a4,a6]
Generators	[6:78:1]	Generators of the group modulo torsion
j	6898185213952/242109	j-invariant
L	4.8905957948354	L(r)(E,1)/r!
Ω	2.3197415403363	Real period
R	2.1082502984908	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	20496a1 81984n1 30744d1 71736i1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10248g1

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

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Quadratic twists for elliptic curve 10248g1

-4	8	-3	-7
20496a1	81984n1	30744d1	71736i1

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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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