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	64	Product of Tamagawa factors cp
Δ	20584214784 = 28 · 32 · 74 · 612	Discriminant
Eigenvalues	2- 3- -2 7-  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1044,10656]	[a1,a2,a3,a4,a6]
Generators	[-30:126:1]	Generators of the group modulo torsion
j	492040858192/80407089	j-invariant
L	4.8905957948354	L(r)(E,1)/r!
Ω	1.1598707701681	Real period
R	1.0541251492454	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	20496a2 81984n2 30744d2 71736i2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10248g2

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 10248g2

-4	8	-3	-7
20496a2	81984n2	30744d2	71736i2

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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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