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	13400g	Isogeny class
Conductor	13400	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	-10720000 = -1 · 28 · 54 · 67	Discriminant
Eigenvalues	2+ -2 5- -2 -4  0 -5 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,163]	[a1,a2,a3,a4,a6]
Generators	[-2:15:1] [-1:14:1]	Generators of the group modulo torsion
j	-25600/67	j-invariant
L	4.6237747822602	L(r)(E,1)/r!
Ω	2.0126574446841	Real period
R	0.19144567606672	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26800p1 107200bl1 120600cf1 13400n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13400g1

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	-4	0	-5	-4	3	-1	4	-6	-12	2	0	4	1	-14	+	-9	-11	-10	-9	-2	8

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Quadratic twists for elliptic curve 13400g1

-4	8	-3	5
26800p1	107200bl1	120600cf1	13400n1

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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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