Cremona's table of elliptic curves

59475 = 3 · 5² · 13 · 61

Class	r	Atkin-Lehner	Eigenvalues
59475a (2 curves)	1	3+ 5+ 13+ 61+	-1 3+ 5+ -2  2 13+ -6  4
Curve Equation t Generators 59475a1 [1,1,1,812,-15844] 2 [40:267:1] 59475a2 [1,1,1,-6813,-183594] 2 [-50:212:1]
59475b (2 curves)	2	3+ 5+ 13+ 61-	0 3+ 5+  1  0 13+ -6 -7
Curve Equation t Generators 59475b1 [0,-1,1,2467,-431032] 1 [1974:-9926:27]&[112:1112:1] 59475b2 [0,-1,1,-363533,-84267907] 1 [697:687:1]&[14906:604171:8]
59475c (3 curves)	0	3+ 5+ 13+ 61-	0 3+ 5+  1 -6 13+ -3  2
Curve Equation t 59475c1 [0,-1,1,-1483,32868] 1 59475c2 [0,-1,1,12017,-483507] 1 59475c3 [0,-1,1,-308233,-66294882] 1
59475d (4 curves)	2	3+ 5+ 13+ 61-	-1 3+ 5+  0  4 13+ -6 -8
Curve Equation t Generators 59475d1 [1,1,1,-488,3656] 2 [-21:82:1]&[-10:92:1] 59475d2 [1,1,1,-1613,-21094] 4 [-30:52:1]&[-218:581:8] 59475d3 [1,1,1,3262,-118594] 2 [35:182:1]&[44:313:1] 59475d4 [1,1,1,-24488,-1485094] 2 [-91:52:1]&[181:140:1]
59475e (2 curves)	0	3+ 5+ 13- 61+	1 3+ 5+  4  0 13-  6 -2
Curve Equation t 59475e1 [1,1,0,-9650,354375] 2 59475e2 [1,1,0,475,1073250] 2
59475f (1 curve)	1	3+ 5+ 13- 61-	0 3+ 5+ -5  0 13-  2  5
Curve Equation t Generators 59475f1 [0,-1,1,-5176033,-4530839157] 1 [35226:1927171:8]
59475g (2 curves)	1	3+ 5+ 13- 61-	1 3+ 5+  2 -4 13- -4 -8
Curve Equation t Generators 59475g1 [1,1,0,2100,1546875] 2 [3794:231855:1] 59475g2 [1,1,0,-188525,30712500] 2 [2270:2115:8]
59475h (2 curves)	1	3+ 5+ 13- 61-	1 3+ 5+ -2 -4 13- -8  0
Curve Equation t Generators 59475h1 [1,1,0,-47287525,-125182040000] 2 [1604223591117480:-1166827627422193115:3036027392] 59475h2 [1,1,0,-756603150,-8010643843125] 2 [-6026988850140:3013353400695:379503424]
59475i (1 curve)	0	3+ 5- 13- 61-	2 3+ 5-  1 -4 13-  4  1
Curve Equation t 59475i1 [0,-1,1,-6708,385193] 1
59475j (2 curves)	2	3- 5+ 13+ 61+	-1 3- 5+ -4 -2 13+  0  0
Curve Equation t Generators 59475j1 [1,0,0,-813,-1008] 2 [-12:90:1]&[-3:39:1] 59475j2 [1,0,0,-8438,296367] 2 [1749:-4937:27]&[-38:769:1]
59475k (4 curves)	1	3- 5+ 13+ 61-	1 3- 5+  4  4 13+ -2 -4
Curve Equation t Generators 59475k1 [1,0,1,974,67823] 2 [18295525185:-191772074936:397065375] 59475k2 [1,0,1,-20151,1039573] 4 [-607886:61906257:54872] 59475k3 [1,0,1,-60776,-4485427] 2 [-18105:150632:125] 59475k4 [1,0,1,-317526,68841073] 2 [205706821395964:-449756915560483:598650818752]
59475l (4 curves)	1	3- 5+ 13+ 61-	1 3- 5+  4 -4 13+  2 -4
Curve Equation t Generators 59475l1 [1,0,1,-30501,2163523] 2 [6772:19091:64] 59475l2 [1,0,1,-495626,134259023] 4 [32807:5924496:1] 59475l3 [1,0,1,-503251,129912773] 2 [-803:4451:1] 59475l4 [1,0,1,-7930001,8594577773] 2 [18113114726:3262256354403:551368]
59475m (4 curves)	1	3- 5+ 13+ 61-	1 3- 5+ -4  4 13+  2  4
Curve Equation t Generators 59475m1 [1,0,1,83249,-4931227] 2 [1033:33887:1] 59475m2 [1,0,1,-381876,-42141227] 4 [72212:1950693:64] 59475m3 [1,0,1,-3058251,2029373023] 2 [3201555326398:144489353176899:1105507304] 59475m4 [1,0,1,-5147501,-4493234977] 2 [10917:1108291:1]
59475n (2 curves)	1	3- 5+ 13- 61+	-1 3- 5+  4  0 13- -2 -2
Curve Equation t Generators 59475n1 [1,0,0,-1744338,886589667] 2 [771:-795:1] 59475n2 [1,0,0,-1734213,897393042] 2 [1053:14937:1]
59475o (1 curve)	2	3- 5- 13+ 61-	-2 3- 5- -1 -4 13+ -4  1
Curve Equation t Generators 59475o1 [0,1,1,-268,2974] 1 [-166:41:8]&[-16:58:1]

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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