Cremona's table of elliptic curves

67 = Prime conductor

Field	Data	Notes
Atkin-Lehner	67-	Signs for the Atkin-Lehner involutions
Class	67a	Isogeny class
Conductor	67	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	5	Modular degree for the optimal curve
Δ	-67 = Prime discriminant	Discriminant
Eigenvalues	2 -2  2 -2 -4  2  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-12,-21]	[a1,a2,a3,a4,a6]
j	-207474688/67	j-invariant
L	1.2737700365451	L(r)(E,1)/r!
Ω	1.2737700365451	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1072a1 4288a1 603f1 1675c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 67a1

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	2	-2	-4	2	3	7	9	-5	-10	-1	0	-2	-1	10	9	-2	-	0	-7	-8	4	7	0

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Quadratic twists for elliptic curve 67a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-67
1072a1	4288a1	603f1	1675c1	3283e1	8107b1	11323c1	19363c1	24187b1	35443b1	56347a1	64387c1	91723b1	112627a1	123883b1	4489b1

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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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