Cremona's table of elliptic curves

13400 = 2³ · 5² · 67

Field	Data	Notes
Atkin-Lehner	2- 5+ 67+	Signs for the Atkin-Lehner involutions
Class	13400l	Isogeny class
Conductor	13400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	22320	Modular degree for the optimal curve
Δ	-46994218750000 = -1 · 24 · 510 · 673	Discriminant
Eigenvalues	2-  0 5+ -2 -2 -4  1  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-23750,-1446875]	[a1,a2,a3,a4,a6]
j	-9481881600/300763	j-invariant
L	0.3838603194554	L(r)(E,1)/r!
Ω	0.1919301597277	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26800g1 107200n1 120600m1 13400i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13400l1

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	+	-2	-2	-4	1	1	-4	-5	-8	-3	0	8	-13	0	5	-2	+	-3	6	-12	7	-9	-4

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Quadratic twists for elliptic curve 13400l1

-4	8	-3	5
26800g1	107200n1	120600m1	13400i1

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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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