Cremona's table of elliptic curves

6240 = 2⁵ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	6240z	Isogeny class
Conductor	6240	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	4228748057664000 = 29 · 34 · 53 · 138	Discriminant
Eigenvalues	2- 3+ 5-  4  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-117520,15226900]	[a1,a2,a3,a4,a6]
j	350584567631475848/8259273550125	j-invariant
L	2.6232221058514	L(r)(E,1)/r!
Ω	0.43720368430856	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6240bf2 12480co4 18720j2 31200p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240z3

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
-	+	-	4	0	-	2	8	4	6	-8	6	-6	-4	4	6	8	-10	4	8	-14	0	12	-6	-6

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Quadratic twists for elliptic curve 6240z3

-4	8	-3	5	13
6240bf2	12480co4	18720j2	31200p3	81120f3

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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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