Cremona's table of elliptic curves

8030 = 2 · 5 · 11 · 73

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11- 73+	Signs for the Atkin-Lehner involutions
Class	8030b	Isogeny class
Conductor	8030	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	13248	Modular degree for the optimal curve
Δ	-150064640 = -1 · 29 · 5 · 11 · 732	Discriminant
Eigenvalues	2+  3 5+  1 11-  4  7 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2680,54080]	[a1,a2,a3,a4,a6]
j	-2129213662543449/150064640	j-invariant
L	3.478143837181	L(r)(E,1)/r!
Ω	1.7390719185905	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	64240i1 72270bf1 40150bc1 88330bb1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 8030b1

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
+	3	+	1	-	4	7	-7	8	3	7	-1	0	4	4	-7	-6	-13	4	-5	+	2	-8	-11	14

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Quadratic twists for elliptic curve 8030b1

-4	-3	5	-11
64240i1	72270bf1	40150bc1	88330bb1

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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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