Cremona's table of elliptic curves

12240 = 2⁴ · 3² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	12240be	Isogeny class
Conductor	12240	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	214151040000000000 = 216 · 39 · 510 · 17	Discriminant
Eigenvalues	2- 3+ 5+  4 -2 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-598563,176847138]	[a1,a2,a3,a4,a6]
Generators	[14061:68138:27]	Generators of the group modulo torsion
j	294172502025843/2656250000	j-invariant
L	4.6939353351526	L(r)(E,1)/r!
Ω	0.31728211529855	Real period
R	7.3971004176138	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	1530a2 48960dy2 12240bi2 61200di2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12240be2

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	-2	-6	-	0	0	6	0	-8	6	-6	-8	6	12	10	-10	6	0	0	-12	0	-8

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Quadratic twists for elliptic curve 12240be2

-4	8	-3	5
1530a2	48960dy2	12240bi2	61200di2

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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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