Cremona's table of elliptic curves

1400 = 2³ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	1400k	Isogeny class
Conductor	1400	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-6722800 = -1 · 24 · 52 · 75	Discriminant
Eigenvalues	2- -2 5+ 7-  1 -4  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28,-147]	[a1,a2,a3,a4,a6]
Generators	[14:49:1]	Generators of the group modulo torsion
j	-6288640/16807	j-invariant
L	2.0566995636517	L(r)(E,1)/r!
Ω	0.96108818013455	Real period
R	0.21399696782908	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	2800d1 11200w1 12600t1 1400d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1400k1

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	+	-	1	-4	0	6	-3	-3	0	-9	2	-9	6	-6	8	-10	1	-7	2	-9	-12	-4	-16

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Quadratic twists for elliptic curve 1400k1

-4	8	-3	5	-7
2800d1	11200w1	12600t1	1400d1	9800bh1

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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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