Cremona's table of elliptic curves

1225 = 5² · 7²

Field	Data	Notes
Atkin-Lehner	5- 7+	Signs for the Atkin-Lehner involutions
Class	1225f	Isogeny class
Conductor	1225	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-720600125 = -1 · 53 · 78	Discriminant
Eigenvalues	-1  1 5- 7+  0 -2 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-393,-3298]	[a1,a2,a3,a4,a6]
j	-9317	j-invariant
L	1.0657897997377	L(r)(E,1)/r!
Ω	0.53289489986884	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	19600dh1 78400ds1 11025bg1 1225e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1225f1

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 1225f1

-4	8	-3	5	-7
19600dh1	78400ds1	11025bg1	1225e1	1225h1

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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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