Cremona's table of elliptic curves

275 = 5² · 11

Field	Data	Notes
Atkin-Lehner	5+ 11-	Signs for the Atkin-Lehner involutions
Class	275b	Isogeny class
Conductor	275	Conductor
∏ cp	5	Product of Tamagawa factors cp
Δ	-2516421875 = -1 · 56 · 115	Discriminant
Eigenvalues	2  1 5+  2 11- -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-258,-2981]	[a1,a2,a3,a4,a6]
j	-122023936/161051	j-invariant
L	2.8380382820443	L(r)(E,1)/r!
Ω	0.56760765640886	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	4400m2 17600e2 2475h2 11a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 275b2

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	-	-4	2	0	1	0	7	-3	-8	6	-8	6	5	12	7	-3	-4	-10	6	15	7

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Quadratic twists for elliptic curve 275b2

-4	8	-3	5	-7	-11	13	17	-19
4400m2	17600e2	2475h2	11a1	13475j2	3025g2	46475a2	79475e2	99275e2

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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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