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	1400b	Isogeny class
Conductor	1400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-2508800 = -1 · 211 · 52 · 72	Discriminant
Eigenvalues	2+ -1 5+ 7- -1  6 -7  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-168,-788]	[a1,a2,a3,a4,a6]
j	-10303010/49	j-invariant
L	1.3250536653528	L(r)(E,1)/r!
Ω	0.66252683267642	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2800b1 11200s1 12600bz1 1400m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1400b1

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	+	-	-1	6	-7	1	8	-6	4	8	-5	0	6	4	-4	6	-5	14	15	14	1	-3	-6

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Quadratic twists for elliptic curve 1400b1

-4	8	-3	5	-7
2800b1	11200s1	12600bz1	1400m1	9800e1

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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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