Cremona's table of elliptic curves

1225 = 5² · 7²

Field	Data	Notes
Atkin-Lehner	5- 7-	Signs for the Atkin-Lehner involutions
Class	1225h	Isogeny class
Conductor	1225	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-6125 = -1 · 53 · 72	Discriminant
Eigenvalues	-1 -1 5- 7-  0  2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-208083,-36621194]	[a1,a2,a3,a4,a6]
Generators	[1190:36857:1]	Generators of the group modulo torsion
j	-162677523113838677	j-invariant
L	1.4478647486797	L(r)(E,1)/r!
Ω	0.11176617751453	Real period
R	6.4772043782725	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	19600dr2 78400eg2 11025bj2 1225g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1225h2

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 1225h2

-4	8	-3	5	-7
19600dr2	78400eg2	11025bj2	1225g2	1225f2

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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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