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
deg	48	Modular degree for the optimal curve
Δ	-16750 = -1 · 2 · 53 · 67	Discriminant
Eigenvalues	2+ -2 5- -1  3 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,2,6]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	1685159/16750	j-invariant
L	1.3009484555499	L(r)(E,1)/r!
Ω	2.8685877137572	Real period
R	1.3605459397084	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5360o1 21440d1 6030u1 3350e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 670b1

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 670b1

-4	8	-3	5	-7	-11	13	-67
5360o1	21440d1	6030u1	3350e1	32830b1	81070x1	113230p1	44890l1

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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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