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	12342f	Isogeny class
Conductor	12342	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	63606126144 = 26 · 3 · 117 · 17	Discriminant
Eigenvalues	2+ 3+ -2  0 11-  4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1091,6285]	[a1,a2,a3,a4,a6]
Generators	[-2:93:1]	Generators of the group modulo torsion
j	81182737/35904	j-invariant
L	2.5175972106463	L(r)(E,1)/r!
Ω	0.99364027443131	Real period
R	2.5337109167472	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	98736dm1 37026bc1 1122f1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 12342f1

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

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Quadratic twists for elliptic curve 12342f1

-4	-3	-11
98736dm1	37026bc1	1122f1

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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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