Cremona's table of elliptic curves

1575 = 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	3+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	1575c	Isogeny class
Conductor	1575	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5907360375 = 39 · 53 · 74	Discriminant
Eigenvalues	1 3+ 5- 7-  0 -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-582,-3799]	[a1,a2,a3,a4,a6]
Generators	[-16:43:1]	Generators of the group modulo torsion
j	8869743/2401	j-invariant
L	3.411774210252	L(r)(E,1)/r!
Ω	0.9916373872777	Real period
R	0.86013654134658	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200de2 100800cg2 1575d2 1575b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1575c2

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	+	-	-	0	-4	2	0	0	-8	-4	-8	-4	-8	-12	6	-8	10	-8	16	-12	-8	16	12	-4

---

Quadratic twists for elliptic curve 1575c2

-4	8	-3	5	-7
25200de2	100800cg2	1575d2	1575b2	11025m2

---

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