Cremona's table of elliptic curves

10640 = 2⁴ · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 19+	Signs for the Atkin-Lehner involutions
Class	10640z	Isogeny class
Conductor	10640	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	2723840 = 212 · 5 · 7 · 19	Discriminant
Eigenvalues	2-  0 5- 7-  4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-227,1314]	[a1,a2,a3,a4,a6]
j	315821241/665	j-invariant
L	2.5587127103757	L(r)(E,1)/r!
Ω	2.5587127103757	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	665b1 42560co1 95760dn1 53200bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10640z1

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	-	-	4	-2	2	+	8	6	8	-6	6	-4	-8	-6	12	-2	-4	12	-6	-12	4	-10	2

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Quadratic twists for elliptic curve 10640z1

-4	8	-3	5	-7
665b1	42560co1	95760dn1	53200bm1	74480bm1

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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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