Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	50400bq	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1.9375453125E+22	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2646300,-6898988000]	[a1,a2,a3,a4,a6]
Generators	[48960646428944504:692126109580043664:20054921267809]	Generators of the group modulo torsion
j	-43927191786304/415283203125	j-invariant
L	5.5548684083371	L(r)(E,1)/r!
Ω	0.051666875594747	Real period
R	26.878286834749	Regulator
r	1	Rank of the group of rational points
S	0.99999999999524	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400dd2 100800fj1 16800bx4 10080by4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bq2

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

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Quadratic twists for elliptic curve 50400bq2

-4	8	-3	5
50400dd2	100800fj1	16800bx4	10080by4

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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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