Cremona's table of elliptic curves

101400 = 2³ · 3 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	101400k	Isogeny class
Conductor	101400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2033051950800000000 = 210 · 34 · 58 · 137	Discriminant
Eigenvalues	2+ 3+ 5+  4  0 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2372761408,-44485809477188]	[a1,a2,a3,a4,a6]
Generators	[-5047252585122170755725555315648210635052107822933935707:140253667167408073701489146285744906142553816295636:179470632974425965570725633103237998181222888712753]	Generators of the group modulo torsion
j	19129597231400697604/26325	j-invariant
L	7.0360352563277	L(r)(E,1)/r!
Ω	0.021631470176232	Real period
R	81.317117971476	Regulator
r	1	Rank of the group of rational points
S	1.0000000010602	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20280y3 7800n3	Quadratic twists by: 5 13

Hecke Eigenvalues for elliptic curve 101400k4

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
+	+	+	4	0	+	-2	0	0	-2	4	6	6	-4	-4	10	0	-2	8	-4	-6	-8	8	6	-14

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Quadratic twists for elliptic curve 101400k4

5	13
20280y3	7800n3

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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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