Cremona's table of elliptic curves

7670 = 2 · 5 · 13 · 59

Field	Data	Notes
Atkin-Lehner	2+ 5- 13+ 59+	Signs for the Atkin-Lehner involutions
Class	7670b	Isogeny class
Conductor	7670	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-199420 = -1 · 22 · 5 · 132 · 59	Discriminant
Eigenvalues	2+ -2 5-  2  0 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3,-22]	[a1,a2,a3,a4,a6]
j	-1771561/199420	j-invariant
L	1.4078580717406	L(r)(E,1)/r!
Ω	1.4078580717406	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	61360o1 69030bi1 38350x1 99710x1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 7670b1

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
+	-2	-	2	0	+	6	4	8	6	10	2	-2	-4	-4	8	+	0	4	4	-10	16	12	-12	18

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Quadratic twists for elliptic curve 7670b1

-4	-3	5	13
61360o1	69030bi1	38350x1	99710x1

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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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