Cremona's table of elliptic curves

1225 = 5² · 7²

Field	Data	Notes
Atkin-Lehner	5- 7-	Signs for the Atkin-Lehner involutions
Class	1225g	Isogeny class
Conductor	1225	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-95703125 = -1 · 59 · 72	Discriminant
Eigenvalues	1  1 5- 7-  0 -2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-5202076,-4567245077]	[a1,a2,a3,a4,a6]
Generators	[4895271887153145073967:1693402407380764960626706:40775428183359871]	Generators of the group modulo torsion
j	-162677523113838677	j-invariant
L	3.4778775075699	L(r)(E,1)/r!
Ω	0.049983354101557	Real period
R	34.790357410824	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19600dv2 78400eu2 11025bl2 1225h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1225g2

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	1	-	-	0	-2	-2	-6	-3	7	-2	-8	-5	7	0	6	-10	-7	-5	-2	6	-2	11	-9	16

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Quadratic twists for elliptic curve 1225g2

-4	8	-3	5	-7
19600dv2	78400eu2	11025bl2	1225h2	1225e2

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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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