Cremona's table of elliptic curves

2175 = 3 · 5² · 29

Class	r	Atkin-Lehner	Eigenvalues
2175a (2 curves)	1	3+ 5+ 29+	0 3+ 5+ -2  3 -2  0  2
Curve Equation t Generators 2175a1 [0,-1,1,-283,1968] 1 [12:12:1] 2175a2 [0,-1,1,1217,7593] 1 [-3:62:1]
2175b (4 curves)	0	3+ 5+ 29-	1 3+ 5+  4  0 -6 -2  8
Curve Equation t 2175b1 [1,1,0,-750,-5625] 2 2175b2 [1,1,0,-10875,-441000] 4 2175b3 [1,1,0,-174000,-28009125] 2 2175b4 [1,1,0,-9750,-534375] 2
2175c (4 curves)	2	3+ 5+ 29-	-1 3+ 5+ -4 -4 -6 -6 -4
Curve Equation t Generators 2175c1 [1,1,1,-688,6656] 4 [-30:52:1]&[-10:117:1] 2175c2 [1,1,1,-813,3906] 4 [-24:113:1]&[-20:122:1] 2175c3 [1,1,1,-6438,-198594] 2 [-50:62:1]&[-44:65:1] 2175c4 [1,1,1,2812,32906] 2 [-10:67:1]&[9:238:1]
2175d (1 curve)	1	3+ 5- 29-	0 3+ 5-  1 -2 -3  4  1
Curve Equation t Generators 2175d1 [0,-1,1,-3833,101318] 1 [-8:362:1]
2175e (2 curves)	1	3+ 5- 29-	-1 3+ 5-  2  0 -4 -2  0
Curve Equation t Generators 2175e1 [1,1,1,-18,6] 2 [0:2:1] 2175e2 [1,1,1,-243,1356] 2 [10:2:1]
2175f (2 curves)	1	3+ 5- 29-	2 3+ 5-  2 -3 -4 -8  0
Curve Equation t Generators 2175f1 [0,-1,1,-17458,-882057] 1 [96803706:659971191:551368] 2175f2 [0,-1,1,28792,-4368307] 1 [12986:525621:8]
2175g (1 curve)	1	3- 5+ 29-	0 3- 5+ -1 -2  3 -4  1
Curve Equation t Generators 2175g1 [0,1,1,-153,749] 1 [27:130:1]
2175h (1 curve)	1	3- 5+ 29-	0 3- 5+  2  1 -6 -4 -2
Curve Equation t Generators 2175h1 [0,1,1,1967,-136406] 1 [278:4687:1]
2175i (2 curves)	0	3- 5- 29-	1 3- 5- -2  0  4  2  0
Curve Equation t 2175i1 [1,0,1,-451,1673] 2 2175i2 [1,0,1,-6076,181673] 2
2175j (2 curves)	0	3- 5- 29-	-2 3- 5- -2 -3  4  8  0
Curve Equation t 2175j1 [0,1,1,-698,-7336] 1 2175j2 [0,1,1,1152,-34486] 5

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