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	50400cp	Isogeny class
Conductor	50400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	1512000 = 26 · 33 · 53 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+  2  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-45,100]	[a1,a2,a3,a4,a6]
Generators	[-1:12:1]	Generators of the group modulo torsion
j	46656/7	j-invariant
L	5.770173146906	L(r)(E,1)/r!
Ω	2.5722130604489	Real period
R	1.1216359242603	Regulator
r	1	Rank of the group of rational points
S	1.0000000000007	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400q1 100800bv1 50400n1 50400p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400cp1

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	2	-6	0	-4	6	-2	2	-6	-2	2	2	0	-4	2	-8	2	4	12	-6	14

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Quadratic twists for elliptic curve 50400cp1

-4	8	-3	5
50400q1	100800bv1	50400n1	50400p1

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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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