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	13400i	Isogeny class
Conductor	13400	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4464	Modular degree for the optimal curve
Δ	-3007630000 = -1 · 24 · 54 · 673	Discriminant
Eigenvalues	2+  0 5-  2 -2  4 -1  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-950,-11575]	[a1,a2,a3,a4,a6]
Generators	[136:1541:1]	Generators of the group modulo torsion
j	-9481881600/300763	j-invariant
L	4.8577585230391	L(r)(E,1)/r!
Ω	0.42916888408353	Real period
R	1.8864984171334	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	26800k1 107200z1 120600ck1 13400l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13400i1

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 13400i1

-4	8	-3	5
26800k1	107200z1	120600ck1	13400l1

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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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