Cremona's table of elliptic curves

1225 = 5² · 7²

Field	Data	Notes
Atkin-Lehner	5- 7-	Signs for the Atkin-Lehner involutions
Class	1225j	Isogeny class
Conductor	1225	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-102942875 = -1 · 53 · 77	Discriminant
Eigenvalues	-2  1 5- 7- -3  1  7  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,82,424]	[a1,a2,a3,a4,a6]
Generators	[23:122:1]	Generators of the group modulo torsion
j	4096/7	j-invariant
L	1.6063817721982	L(r)(E,1)/r!
Ω	1.2922000138736	Real period
R	0.15539213695165	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	19600dw1 78400ew1 11025bo1 1225i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1225j1

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

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Quadratic twists for elliptic curve 1225j1

-4	8	-3	5	-7
19600dw1	78400ew1	11025bo1	1225i1	175a1

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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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