Cremona's table of elliptic curves

7448 = 2³ · 7² · 19

Field	Data	Notes
Atkin-Lehner	2- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	7448n	Isogeny class
Conductor	7448	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-95121819184 = -1 · 24 · 74 · 195	Discriminant
Eigenvalues	2- -2 -1 7+ -1  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3691,86358]	[a1,a2,a3,a4,a6]
Generators	[191:-2527:1]	Generators of the group modulo torsion
j	-144797599744/2476099	j-invariant
L	2.5154339545728	L(r)(E,1)/r!
Ω	1.0701409085608	Real period
R	0.078352110282865	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14896d1 59584e1 67032k1 7448s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7448n1

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	-1	+	-1	2	-2	-	-3	4	4	-10	10	1	1	-4	8	3	-4	-4	-3	14	-9	6	-14

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Quadratic twists for elliptic curve 7448n1

-4	8	-3	-7
14896d1	59584e1	67032k1	7448s1

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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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