Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	1600c	Isogeny class
Conductor	1600	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-20480000000000 = -1 · 221 · 510	Discriminant
Eigenvalues	2+  1 5+ -2  3 -4  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-200833,-34709537]	[a1,a2,a3,a4,a6]
Generators	[31593:986048:27]	Generators of the group modulo torsion
j	-349938025/8	j-invariant
L	3.0954235363659	L(r)(E,1)/r!
Ω	0.11276128443925	Real period
R	6.8627799686722	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1600q4 50b4 14400bh4 1600j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1600c4

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
+	1	+	-2	3	-4	3	-5	-6	0	2	2	-3	-4	-12	6	0	-2	-13	12	-11	-10	-9	15	-2

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Quadratic twists for elliptic curve 1600c4

-4	8	-3	5	-7
1600q4	50b4	14400bh4	1600j2	78400bp4

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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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