Cremona's table of elliptic curves

1357 = 23 · 59

Field	Data	Notes
Atkin-Lehner	23+ 59+	Signs for the Atkin-Lehner involutions
Class	1357a	Isogeny class
Conductor	1357	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-31211 = -1 · 232 · 59	Discriminant
Eigenvalues	-1  1 -3  1  0  4 -2  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-52,-149]	[a1,a2,a3,a4,a6]
Generators	[9:7:1]	Generators of the group modulo torsion
j	-15568817473/31211	j-invariant
L	1.8062341392833	L(r)(E,1)/r!
Ω	0.8887365900296	Real period
R	1.0161808119226	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21712j1 86848e1 12213b1 33925c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1357a1

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	1	-3	1	0	4	-2	7	+	-7	4	-2	-5	2	-2	1	+	-10	-10	0	-10	-13	10	-12	-2

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Quadratic twists for elliptic curve 1357a1

-4	8	-3	5	-7	-23	-59
21712j1	86848e1	12213b1	33925c1	66493c1	31211a1	80063a1

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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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