Cremona's table of elliptic curves

670 = 2 · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 5+ 67-	Signs for the Atkin-Lehner involutions
Class	670c	Isogeny class
Conductor	670	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-10720 = -1 · 25 · 5 · 67	Discriminant
Eigenvalues	2-  0 5+ -5 -3  6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-13,21]	[a1,a2,a3,a4,a6]
Generators	[3:-4:1]	Generators of the group modulo torsion
j	-225866529/10720	j-invariant
L	2.6312306771696	L(r)(E,1)/r!
Ω	4.0108342189201	Real period
R	0.13120615480727	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5360h1 21440h1 6030m1 3350b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 670c1

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
-	0	+	-5	-3	6	-6	-2	-4	0	-4	7	-2	2	2	4	6	-13	-	-15	-8	-14	9	-15	3

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Quadratic twists for elliptic curve 670c1

-4	8	-3	5	-7	-11	13	-67
5360h1	21440h1	6030m1	3350b1	32830m1	81070e1	113230j1	44890d1

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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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