Cremona's table of elliptic curves

12342 = 2 · 3 · 11² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 17-	Signs for the Atkin-Lehner involutions
Class	12342v	Isogeny class
Conductor	12342	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	460800	Modular degree for the optimal curve
Δ	1.2251128379213E+19	Discriminant
Eigenvalues	2- 3+  2 -4 11- -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1001822,346858139]	[a1,a2,a3,a4,a6]
j	62768149033310713/6915442583808	j-invariant
L	1.7464496680397	L(r)(E,1)/r!
Ω	0.21830620850496	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	98736dj1 37026m1 1122b1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 12342v1

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	-4	-	-6	-	-4	0	-2	0	-10	10	4	4	-2	0	-2	12	0	10	-4	12	-14	18

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Quadratic twists for elliptic curve 12342v1

-4	-3	-11
98736dj1	37026m1	1122b1

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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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