Cremona's table of elliptic curves

40800 = 2⁵ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 17-	Signs for the Atkin-Lehner involutions
Class	40800q	Isogeny class
Conductor	40800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	88465794624000 = 29 · 314 · 53 · 172	Discriminant
Eigenvalues	2+ 3+ 5-  2  6 -6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11768,195432]	[a1,a2,a3,a4,a6]
Generators	[1194:10557:8]	Generators of the group modulo torsion
j	2816362943848/1382278041	j-invariant
L	5.5710435132344	L(r)(E,1)/r!
Ω	0.53669533305565	Real period
R	5.1901359766966	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40800bd2 81600jt2 122400ec2 40800bx2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800q2

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
+	+	-	2	6	-6	-	4	0	-8	-8	2	-10	0	12	-10	2	2	4	8	0	16	4	6	-12

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Quadratic twists for elliptic curve 40800q2

-4	8	-3	5
40800bd2	81600jt2	122400ec2	40800bx2

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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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