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	50400h	Isogeny class
Conductor	50400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	3444525000000 = 26 · 39 · 58 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7425,229500]	[a1,a2,a3,a4,a6]
j	2299968/175	j-invariant
L	3.1004797259021	L(r)(E,1)/r!
Ω	0.77511993145097	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400ce1 100800q2 50400ck1 10080bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400h1

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 50400h1

-4	8	-3	5
50400ce1	100800q2	50400ck1	10080bi1

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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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