Cremona's table of elliptic curves

75 = 3 · 5²

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	75c	Isogeny class
Conductor	75	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-6075 = -1 · 35 · 52	Discriminant
Eigenvalues	-2 3- 5+  3  2 -1 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,2,4]	[a1,a2,a3,a4,a6]
j	20480/243	j-invariant
L	0.62723492949639	L(r)(E,1)/r!
Ω	3.136174647482	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	1200k1 4800e1 225d1 75a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75c1

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
-2	-	+	3	2	-1	-2	-5	-6	10	-3	-2	-8	-1	-2	4	-10	7	3	-8	14	0	-6	0	-17

---

Quadratic twists for elliptic curve 75c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200k1	4800e1	225d1	75a2	3675f1	9075n1	12675bb1	21675i1	27075i1	39675bi1	63075d1	72075m1	102675t1	126075l1

---

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