Cremona's table of elliptic curves

2530 = 2 · 5 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 11- 23+	Signs for the Atkin-Lehner involutions
Class	2530i	Isogeny class
Conductor	2530	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	-1355819922325000 = -1 · 23 · 55 · 119 · 23	Discriminant
Eigenvalues	2- -2 5+ -1 11-  2  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1331,1771561]	[a1,a2,a3,a4,a6]
Generators	[88:1485:1]	Generators of the group modulo torsion
j	-260782396264369/1355819922325000	j-invariant
L	3.1950903617871	L(r)(E,1)/r!
Ω	0.38597590995421	Real period
R	2.7593175976243	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	20240m1 80960t1 22770u1 12650m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2530i1

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	+	-1	-	2	0	-1	+	3	-4	-10	-6	8	9	-6	-9	2	-7	-12	-7	-10	12	6	5

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Quadratic twists for elliptic curve 2530i1

-4	8	-3	5	-7	-11	-23
20240m1	80960t1	22770u1	12650m1	123970by1	27830d1	58190bd1

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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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