Cremona's table of elliptic curves

45 = 3² · 5

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	45a	Isogeny class
Conductor	45	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	295245 = 310 · 5	Discriminant
Eigenvalues	1 3- 5+  0  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-19440,1048135]	[a1,a2,a3,a4,a6]
j	1114544804970241/405	j-invariant
L	0.92159087663963	L(r)(E,1)/r!
Ω	1.8431817532793	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	720h7 2880r7 15a5 225c7	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 45a7

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

---

Quadratic twists for elliptic curve 45a7

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
720h7	2880r7	15a5	225c7	2205j7	5445g7	7605q7	13005n7	16245d7	23805t8	37845d8	43245b8	61605k8	75645g8	83205u8	99405m8	126405s8

---

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