Cremona's table of elliptic curves

75 = 3 · 5²

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	75b	Isogeny class
Conductor	75	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-234375 = -1 · 3 · 57	Discriminant
Eigenvalues	1 3- 5+  0 -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1,23]	[a1,a2,a3,a4,a6]
j	-1/15	j-invariant
L	1.2527374448595	L(r)(E,1)/r!
Ω	2.505474889719	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	1200j1 4800b1 225c1 15a8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 75b1

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

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Quadratic twists for elliptic curve 75b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200j1	4800b1	225c1	15a8	3675e1	9075l1	12675x1	21675c1	27075g1	39675bc1	63075c1	72075f1	102675s1	126075c1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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