Cremona's table of elliptic curves

1225 = 5² · 7²

Field	Data	Notes
Atkin-Lehner	5+ 7-	Signs for the Atkin-Lehner involutions
Class	1225b	Isogeny class
Conductor	1225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-5359375 = -1 · 56 · 73	Discriminant
Eigenvalues	-1  0 5+ 7-  4  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-55,-178]	[a1,a2,a3,a4,a6]
j	-3375	j-invariant
L	0.86460327909105	L(r)(E,1)/r!
Ω	0.86460327909105	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19600cb1 78400v1 11025y1 49a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1225b1

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	0	+	-	4	0	0	0	-8	2	0	6	0	12	0	10	0	0	-4	16	0	8	0	0	0

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Quadratic twists for elliptic curve 1225b1

-4	8	-3	5	-7
19600cb1	78400v1	11025y1	49a1	1225b3

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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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