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	1230b	Isogeny class
Conductor	1230	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	1800	Modular degree for the optimal curve
Δ	-94128829920 = -1 · 25 · 315 · 5 · 41	Discriminant
Eigenvalues	2+ 3- 5+ -1  6 -4  0  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,121,14762]	[a1,a2,a3,a4,a6]
j	198257271191/94128829920	j-invariant
L	1.3862582616675	L(r)(E,1)/r!
Ω	0.83175495700053	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	9840k1 39360k1 3690u1 6150t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230b1

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	6	-4	0	5	-3	6	-1	-7	+	11	12	9	9	8	-4	12	2	-16	12	-15	2

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Quadratic twists for elliptic curve 1230b1

-4	8	-3	5	-7	41
9840k1	39360k1	3690u1	6150t1	60270g1	50430c1

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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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