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	10640f	Isogeny class
Conductor	10640	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	12045501440 = 210 · 5 · 73 · 193	Discriminant
Eigenvalues	2+  0 5- 7+ -4 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-250947947,-1530113279126]	[a1,a2,a3,a4,a6]
Generators	[50829965242955067183450:11695614712593536916232921:880214980371893928]	Generators of the group modulo torsion
j	1706768805632178182685889284/11763185	j-invariant
L	4.1755937698099	L(r)(E,1)/r!
Ω	0.037931816672173	Real period
R	36.693855239413	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	5320e4 42560bw4 95760v4 53200r4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10640f3

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

---

Quadratic twists for elliptic curve 10640f3

-4	8	-3	5	-7
5320e4	42560bw4	95760v4	53200r4	74480c4

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations