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	50400ck	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	4725000000 = 26 · 33 · 58 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0  4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-825,-8500]	[a1,a2,a3,a4,a6]
Generators	[40:150:1]	Generators of the group modulo torsion
j	2299968/175	j-invariant
L	6.7046946286127	L(r)(E,1)/r!
Ω	0.89510051444734	Real period
R	1.8726094221762	Regulator
r	1	Rank of the group of rational points
S	1.0000000000026	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400b1 100800r2 50400h1 10080b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400ck1

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
-	+	+	-	0	4	-2	-2	2	-4	10	-6	6	4	-12	-6	-12	6	-4	4	8	0	4	-18	12

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Quadratic twists for elliptic curve 50400ck1

-4	8	-3	5
50400b1	100800r2	50400h1	10080b1

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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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