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	1400j	Isogeny class
Conductor	1400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-140000000 = -1 · 28 · 57 · 7	Discriminant
Eigenvalues	2-  1 5+ 7- -5 -1 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,563]	[a1,a2,a3,a4,a6]
Generators	[13:50:1]	Generators of the group modulo torsion
j	-1024/35	j-invariant
L	3.0380330159698	L(r)(E,1)/r!
Ω	1.5334543984115	Real period
R	0.24764618197295	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	2800c1 11200v1 12600w1 280a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1400j1

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
-	1	+	-	-5	-1	-3	-6	6	-9	0	-6	8	-6	-3	12	8	-4	4	8	-10	-3	12	-16	-7

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Quadratic twists for elliptic curve 1400j1

-4	8	-3	5	-7
2800c1	11200v1	12600w1	280a1	9800bf1

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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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