Cremona's table of elliptic curves

30576 = 2⁴ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	30576bm	Isogeny class
Conductor	30576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-1044291948650496 = -1 · 213 · 35 · 79 · 13	Discriminant
Eigenvalues	2- 3+  1 7-  1 13+  1  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-85080,-9649296]	[a1,a2,a3,a4,a6]
Generators	[356:2248:1]	Generators of the group modulo torsion
j	-141339344329/2167074	j-invariant
L	5.2538691507893	L(r)(E,1)/r!
Ω	0.13964216009648	Real period
R	4.7029754008023	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3822l1 122304hz1 91728dy1 4368z1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576bm1

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	+	1	7	-3	-3	8	7	-8	-7	8	-10	4	-7	-2	-4	1	-2	-6	-14	14

---

Quadratic twists for elliptic curve 30576bm1

-4	8	-3	-7
3822l1	122304hz1	91728dy1	4368z1

---

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