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	13400d	Isogeny class
Conductor	13400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	53760	Modular degree for the optimal curve
Δ	-2617187500000000 = -1 · 28 · 516 · 67	Discriminant
Eigenvalues	2+  0 5+  2 -2 -6 -1  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-100700,-12543500]	[a1,a2,a3,a4,a6]
j	-28232681739264/654296875	j-invariant
L	1.0705500013731	L(r)(E,1)/r!
Ω	0.13381875017164	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	26800b1 107200b1 120600bw1 2680c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13400d1

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	-6	-1	1	-1	-5	-8	3	10	2	-7	0	-5	8	-	12	-11	8	-12	11	-6

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Quadratic twists for elliptic curve 13400d1

-4	8	-3	5
26800b1	107200b1	120600bw1	2680c1

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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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