Cremona's table of elliptic curves

124 = 2² · 31

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	124a	Isogeny class
Conductor	124	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-496 = -1 · 24 · 31	Discriminant
Eigenvalues	2- -2 -3 -1 -6  2  6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2,1]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	-87808/31	j-invariant
L	0.85598274932061	L(r)(E,1)/r!
Ω	4.9333272334189	Real period
R	0.52053069388267	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	496d1 1984f1 1116e1 3100e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 124a1

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	-3	-1	-6	2	6	-1	-6	0	-	-10	-9	8	0	0	-3	-10	-4	-15	14	8	6	12	-7

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Quadratic twists for elliptic curve 124a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
496d1	1984f1	1116e1	3100e1	6076a1	15004d1	20956c1	35836c1	44764b1	65596d1	104284c1	3844c1

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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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