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	1953c	Isogeny class
Conductor	1953	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-9966159 = -1 · 38 · 72 · 31	Discriminant
Eigenvalues	-1 3-  2 7+  2 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,31,128]	[a1,a2,a3,a4,a6]
Generators	[4:15:1]	Generators of the group modulo torsion
j	4657463/13671	j-invariant
L	2.1350503021182	L(r)(E,1)/r!
Ω	1.6140475262381	Real period
R	1.3227927105061	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	31248bz1 124992cd1 651c1 48825bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1953c1

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	-	2	+	2	-4	0	-4	-2	2	-	-2	-6	-2	8	-2	4	-4	0	-12	4	-2	-8	0	-2

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Quadratic twists for elliptic curve 1953c1

-4	8	-3	5	-7	-31
31248bz1	124992cd1	651c1	48825bh1	13671l1	60543h1

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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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