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	1230a	Isogeny class
Conductor	1230	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	2757260250 = 2 · 38 · 53 · 412	Discriminant
Eigenvalues	2+ 3+ 5- -2  2 -2 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1402,19474]	[a1,a2,a3,a4,a6]
Generators	[33:86:1]	Generators of the group modulo torsion
j	305106651317161/2757260250	j-invariant
L	1.7550817838814	L(r)(E,1)/r!
Ω	1.4419983712321	Real period
R	0.40570590991301	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	9840ba2 39360bc2 3690p2 6150bd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230a2

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	2	-2	-4	2	0	-4	0	-6	-	-4	6	10	0	-14	-4	0	-14	-12	4	6	-16

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Quadratic twists for elliptic curve 1230a2

-4	8	-3	5	-7	41
9840ba2	39360bc2	3690p2	6150bd2	60270i2	50430n2

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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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