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	1953g	Isogeny class
Conductor	1953	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-3113712819 = -1 · 315 · 7 · 31	Discriminant
Eigenvalues	0 3-  3 7-  0  5  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,204,2439]	[a1,a2,a3,a4,a6]
j	1287913472/4271211	j-invariant
L	2.0107681293414	L(r)(E,1)/r!
Ω	1.0053840646707	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	31248bk1 124992dk1 651e1 48825w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1953g1

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
0	-	3	-	0	5	0	2	-3	-3	-	2	-9	8	0	3	12	-1	5	6	-7	8	-6	12	-10

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Quadratic twists for elliptic curve 1953g1

-4	8	-3	5	-7	-31
31248bk1	124992dk1	651e1	48825w1	13671j1	60543n1

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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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