Cremona's table of elliptic curves

630 = 2 · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	630j	Isogeny class
Conductor	630	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	1224720 = 24 · 37 · 5 · 7	Discriminant
Eigenvalues	2- 3- 5- 7+  4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-32,51]	[a1,a2,a3,a4,a6]
j	4826809/1680	j-invariant
L	2.5079578706306	L(r)(E,1)/r!
Ω	2.5079578706306	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5040bo1 20160bf1 210d1 3150o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 630j1

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
-	-	-	+	4	-2	6	0	8	-10	-8	2	2	8	-4	-10	-4	-6	0	12	-6	-8	4	-14	2

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Quadratic twists for elliptic curve 630j1

-4	8	-3	5	-7	-11	13
5040bo1	20160bf1	210d1	3150o1	4410be1	76230cl1	106470bu1

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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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