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	1575g	Isogeny class
Conductor	1575	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-196994059171875 = -1 · 37 · 56 · 78	Discriminant
Eigenvalues	-1 3- 5+ 7- -4  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7655,724722]	[a1,a2,a3,a4,a6]
Generators	[140:-1614:1]	Generators of the group modulo torsion
j	-4354703137/17294403	j-invariant
L	1.8654060060321	L(r)(E,1)/r!
Ω	0.49341543970829	Real period
R	0.23628744865774	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	25200dx5 100800fm5 525b6 63a6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1575g6

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	-	+	-	-4	2	-6	4	0	2	0	-6	-2	4	0	6	-12	-2	-4	0	6	-16	-12	14	-18

---

Quadratic twists for elliptic curve 1575g6

-4	8	-3	5	-7
25200dx5	100800fm5	525b6	63a6	11025ba6

---

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