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	670d	Isogeny class
Conductor	670	Conductor
∏ cp	19	Product of Tamagawa factors cp
deg	304	Modular degree for the optimal curve
Δ	-175636480 = -1 · 219 · 5 · 67	Discriminant
Eigenvalues	2- -2 5+  1 -3 -4  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,44,-624]	[a1,a2,a3,a4,a6]
Generators	[8:12:1]	Generators of the group modulo torsion
j	9407293631/175636480	j-invariant
L	2.2406781478657	L(r)(E,1)/r!
Ω	0.87867392636108	Real period
R	0.13421409842378	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	5360j1 21440k1 6030k1 3350c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 670d1

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	+	1	-3	-4	4	-2	-8	-10	-10	1	8	4	-4	-6	0	-3	-	-9	14	6	5	13	19

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Quadratic twists for elliptic curve 670d1

-4	8	-3	5	-7	-11	13	-67
5360j1	21440k1	6030k1	3350c1	32830p1	81070h1	113230k1	44890f1

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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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