Cremona's table of elliptic curves

1953 = 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	3- 7- 31+	Signs for the Atkin-Lehner involutions
Class	1953f	Isogeny class
Conductor	1953	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-102983643 = -1 · 37 · 72 · 312	Discriminant
Eigenvalues	-1 3- -4 7- -2 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,103,-300]	[a1,a2,a3,a4,a6]
Generators	[8:27:1]	Generators of the group modulo torsion
j	167284151/141267	j-invariant
L	1.4969902100454	L(r)(E,1)/r!
Ω	1.0421804034396	Real period
R	0.35910054658116	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31248bt2 124992cx2 651b2 48825p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1953f2

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
-1	-	-4	-	-2	-2	-2	8	6	0	+	6	-8	-4	2	-4	6	-6	-4	-4	-10	12	16	-2	-10

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Quadratic twists for elliptic curve 1953f2

-4	8	-3	5	-7	-31
31248bt2	124992cx2	651b2	48825p2	13671r2	60543r2

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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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