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	1230d	Isogeny class
Conductor	1230	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	8302500 = 22 · 34 · 54 · 41	Discriminant
Eigenvalues	2+ 3- 5- -2  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-53,-52]	[a1,a2,a3,a4,a6]
Generators	[-6:10:1]	Generators of the group modulo torsion
j	16022066761/8302500	j-invariant
L	2.2953078485403	L(r)(E,1)/r!
Ω	1.8765597661984	Real period
R	0.15289333504617	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	9840s1 39360c1 3690s1 6150u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230d1

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

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Quadratic twists for elliptic curve 1230d1

-4	8	-3	5	-7	41
9840s1	39360c1	3690s1	6150u1	60270c1	50430h1

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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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