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	670b	Isogeny class
Conductor	670	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-12030520 = -1 · 23 · 5 · 673	Discriminant
Eigenvalues	2+ -2 5- -1  3 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-23,-174]	[a1,a2,a3,a4,a6]
Generators	[22:89:1]	Generators of the group modulo torsion
j	-1263214441/12030520	j-invariant
L	1.3009484555499	L(r)(E,1)/r!
Ω	0.95619590458575	Real period
R	0.45351531323612	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	5360o2 21440d2 6030u2 3350e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 670b2

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	0	2	0	-6	2	-7	-12	-4	0	-6	-12	11	-	-9	-10	2	-3	-3	5

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Quadratic twists for elliptic curve 670b2

-4	8	-3	5	-7	-11	13	-67
5360o2	21440d2	6030u2	3350e2	32830b2	81070x2	113230p2	44890l2

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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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