Cremona's table of elliptic curves

31857 = 3 · 7 · 37 · 41

Class	r	Atkin-Lehner	Eigenvalues
31857a (1 curve)	1	3+ 7- 37+ 41-	0 3+ -3 7-  3  1  2  4
Curve Equation t Generators 31857a1 [0,-1,1,163,257] 1 [1:20:1]
31857b (2 curves)	1	3- 7+ 37+ 41-	-1 3- -2 7+  0 -4 -4 -2
Curve Equation t Generators 31857b1 [1,0,0,-389,-2976] 2 [-11:7:1] 31857b2 [1,0,0,-574,95] 2 [-13:80:1]
31857c (4 curves)	1	3- 7+ 37- 41+	-1 3- -2 7+  0  2  6 -4
Curve Equation t Generators 31857c1 [1,0,0,-7699,-256312] 2 [113:509:1] 31857c2 [1,0,0,-16104,400959] 4 [-15:807:1] 31857c3 [1,0,0,54211,2974488] 2 [31:2149:1] 31857c4 [1,0,0,-220899,39926394] 2 [318:1206:1]
31857d (2 curves)	0	3- 7+ 37- 41-	1 3- -4 7+  0  6  6  0
Curve Equation t 31857d1 [1,0,1,-14248,-1087543] 2 31857d2 [1,0,1,-267513,-53260133] 2
31857e (1 curve)	2	3- 7+ 37- 41-	-2 3- -1 7+ -3 -3 -6  0
Curve Equation t Generators 31857e1 [0,1,1,-17886,917732] 1 [-135:943:1]&[198:-2276:1]
31857f (2 curves)	0	3- 7- 37- 41+	-1 3- -4 7-  4 -6 -2  4
Curve Equation t 31857f1 [1,0,0,-105,-504] 2 31857f2 [1,0,0,-1770,-28809] 2

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

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