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	50400bp	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	8037225000000 = 26 · 38 · 58 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5925,110500]	[a1,a2,a3,a4,a6]
Generators	[-60:500:1]	Generators of the group modulo torsion
j	31554496/11025	j-invariant
L	6.2779653047025	L(r)(E,1)/r!
Ω	0.6778107616599	Real period
R	2.3155302555612	Regulator
r	1	Rank of the group of rational points
S	1.0000000000046	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	50400dj1 100800fv2 16800ca1 10080bx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400bp1

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

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Quadratic twists for elliptic curve 50400bp1

-4	8	-3	5
50400dj1	100800fv2	16800ca1	10080bx1

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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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