Cremona's table of elliptic curves

12075 = 3 · 5² · 7 · 23

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 23+	Signs for the Atkin-Lehner involutions
Class	12075c	Isogeny class
Conductor	12075	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	25344	Modular degree for the optimal curve
Δ	11477853515625 = 3 · 59 · 7 · 234	Discriminant
Eigenvalues	1 3+ 5+ 7+  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5775,42000]	[a1,a2,a3,a4,a6]
Generators	[-16760:235805:512]	Generators of the group modulo torsion
j	1363569097969/734582625	j-invariant
L	4.4416553960906	L(r)(E,1)/r!
Ω	0.62594075534641	Real period
R	7.0959677224285	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	36225bk1 2415f1 84525by1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12075c1

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

---

Quadratic twists for elliptic curve 12075c1

-3	5	-7
36225bk1	2415f1	84525by1

---

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