Cremona's table of elliptic curves

700 = 2² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	700a	Isogeny class
Conductor	700	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-6860000000 = -1 · 28 · 57 · 73	Discriminant
Eigenvalues	2- -1 5+ 7+  3  1  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-20133,-1092863]	[a1,a2,a3,a4,a6]
j	-225637236736/1715	j-invariant
L	1.2023798522741	L(r)(E,1)/r!
Ω	0.20039664204568	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	2800t2 11200d2 6300h2 140a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 700a2

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	+	+	3	1	3	2	6	-9	8	10	0	-2	3	0	12	8	-8	0	-14	5	12	12	-17

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Quadratic twists for elliptic curve 700a2

-4	8	-3	5	-7	-11	13
2800t2	11200d2	6300h2	140a2	4900f2	84700p2	118300u2

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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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