Cremona's table of elliptic curves

3120 = 2⁴ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	3120a	Isogeny class
Conductor	3120	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	47971512576000 = 211 · 38 · 53 · 134	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9896,183696]	[a1,a2,a3,a4,a6]
Generators	[-80:676:1]	Generators of the group modulo torsion
j	52337949619538/23423590125	j-invariant
L	2.7398327179869	L(r)(E,1)/r!
Ω	0.57131577520162	Real period
R	1.1989134717224	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	1560c3 12480db3 9360q3 15600r3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3120a3

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
+	+	+	0	0	+	2	0	-4	6	-8	10	-6	-4	8	2	0	6	-12	-8	6	-8	12	-14	-10

---

Quadratic twists for elliptic curve 3120a3

-4	8	-3	5	13
1560c3	12480db3	9360q3	15600r3	40560h4

---

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