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	700j	Isogeny class
Conductor	700	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-3500000000 = -1 · 28 · 59 · 7	Discriminant
Eigenvalues	2-  3 5- 7-  3  1 -5 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1000,12500]	[a1,a2,a3,a4,a6]
j	-221184/7	j-invariant
L	2.8009323280638	L(r)(E,1)/r!
Ω	1.4004661640319	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	2800bb1 11200bs1 6300bc1 700g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 700j1

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
-	3	-	-	3	1	-5	-8	2	-1	-2	10	-6	-4	11	6	-10	0	-10	0	-10	-7	12	8	3

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Quadratic twists for elliptic curve 700j1

-4	8	-3	5	-7	-11	13
2800bb1	11200bs1	6300bc1	700g1	4900w1	84700bd1	118300bi1

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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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