Cremona's table of elliptic curves

75 = 3 · 5²

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Conductor	75	Conductor
Count	8	Number of curves in isogeny class
Curves	75b1 75b2 75b3 75b4 75b5 75b6 75b7 75b8	Curves in isogeny class
deg	6	Modular degree for the optimal curve
Eigenvalues	1 3- 5+  0 -4  2 -2  4	Hecke eigenvalues for primes less than 20
L	1.2527374448595	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	1200j 4800b 225c 15a	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 75b

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 isogeny class 75b

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41
1200j	4800b	225c	15a	3675e	9075l	12675x	21675c	27075g	39675bc	63075c	72075f	102675s	126075c

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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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