Cremona's table of elliptic curves

2431 = 11 · 13 · 17

Field	Data	Notes
Atkin-Lehner	11- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	2431b	Isogeny class
Conductor	2431	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-31603 = -1 · 11 · 132 · 17	Discriminant
Eigenvalues	0 -2 -4 -1 11- 13+ 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-55,140]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	-18736316416/31603	j-invariant
L	1.1593366211832	L(r)(E,1)/r!
Ω	3.7032578820397	Real period
R	0.15652928557931	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	38896g1 21879h1 60775n1 119119l1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2431b1

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	-2	-4	-1	-	+	-	-4	0	3	2	2	-3	12	-7	5	-1	10	-7	2	-11	16	0	3	0

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Quadratic twists for elliptic curve 2431b1

-4	-3	5	-7	-11	13	17
38896g1	21879h1	60775n1	119119l1	26741e1	31603e1	41327b1

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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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