Cremona's table of elliptic curves

1230 = 2 · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 41+	Signs for the Atkin-Lehner involutions
Class	1230k	Isogeny class
Conductor	1230	Conductor
∏ cp	343	Product of Tamagawa factors cp
deg	1960	Modular degree for the optimal curve
Δ	-896670000000 = -1 · 27 · 37 · 57 · 41	Discriminant
Eigenvalues	2- 3- 5-  1 -2  0  4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2305,-15975]	[a1,a2,a3,a4,a6]
j	1354330706847119/896670000000	j-invariant
L	3.532526713973	L(r)(E,1)/r!
Ω	0.50464667342472	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	7	Number of elements in the torsion subgroup
Twists	9840r1 39360b1 3690g1 6150a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230k1

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
-	-	-	1	-2	0	4	-1	3	2	11	-11	+	-5	-8	5	11	-8	12	-12	-10	-4	0	-15	14

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Quadratic twists for elliptic curve 1230k1

-4	8	-3	5	-7	41
9840r1	39360b1	3690g1	6150a1	60270t1	50430u1

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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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