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
deg	48	Modular degree for the optimal curve
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,-8,6]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	-9317	j-invariant
L	1.4478647486797	L(r)(E,1)/r!
Ω	4.1353485680374	Real period
R	0.17505957779115	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	19600dr1 78400eg1 11025bj1 1225g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1225h1

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

---

Quadratic twists for elliptic curve 1225h1

-4	8	-3	5	-7
19600dr1	78400eg1	11025bj1	1225g1	1225f1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations