Cremona's table of elliptic curves

7728 = 2⁴ · 3 · 7 · 23

Class	r	Atkin-Lehner	Eigenvalues
7728a (2 curves)	1	2+ 3+ 7+ 23+	2+ 3+  2 7+ -4  4  4 -6
Curve Equation t Generators 7728a1 [0,-1,0,128,592] 2 [-2:18:1] 7728a2 [0,-1,0,-792,6480] 2 [2:70:1]
7728b (4 curves)	0	2+ 3+ 7+ 23-	2+ 3+  2 7+  0  6 -6  0
Curve Equation t 7728b1 [0,-1,0,268,1152] 2 7728b2 [0,-1,0,-1352,11520] 4 7728b3 [0,-1,0,-9632,-352800] 2 7728b4 [0,-1,0,-18992,1013472] 4
7728c (1 curve)	0	2+ 3+ 7+ 23-	2+ 3+  4 7+ -3 -2  4  7
Curve Equation t 7728c1 [0,-1,0,-201,1173] 1
7728d (1 curve)	0	2+ 3+ 7- 23+	2+ 3+  0 7- -1 -6  0 -7
Curve Equation t 7728d1 [0,-1,0,7,-459] 1
7728e (2 curves)	1	2+ 3- 7- 23+	2+ 3-  0 7-  2 -6 -6  6
Curve Equation t Generators 7728e1 [0,1,0,-1568,44100] 2 [-14:252:1] 7728e2 [0,1,0,-30728,2061972] 2 [-62:1932:1]
7728f (1 curve)	1	2+ 3- 7- 23+	2+ 3- -3 7-  0 -1 -4  0
Curve Equation t Generators 7728f1 [0,1,0,-392,4116] 1 [-14:84:1]
7728g (1 curve)	0	2- 3+ 7+ 23+	2- 3+  0 7+ -1  2  4  3
Curve Equation t 7728g1 [0,-1,0,27,-51] 1
7728h (4 curves)	0	2- 3+ 7+ 23+	2- 3+  0 7+ -6  2 -6 -2
Curve Equation t 7728h1 [0,-1,0,74312,-54937232] 2 7728h2 [0,-1,0,-1791928,-879068816] 2 7728h3 [0,-1,0,-670888,1508909680] 2 7728h4 [0,-1,0,-24263848,45788177008] 2
7728i (2 curves)	1	2- 3+ 7+ 23-	2- 3+  0 7+ -3  2  0 -5
Curve Equation t Generators 7728i1 [0,-1,0,-478493,-127241151] 1 [6441:513774:1] 7728i2 [0,-1,0,-148013,-299020767] 1 [1509:53958:1]
7728j (2 curves)	1	2- 3+ 7+ 23-	2- 3+ -3 7+  0  5  0 -8
Curve Equation t Generators 7728j1 [0,-1,0,48,-576] 1 [8:16:1] 7728j2 [0,-1,0,-432,15936] 1 [32:-184:1]
7728k (2 curves)	1	2- 3+ 7- 23+	2- 3+  0 7-  2 -6  2  6
Curve Equation t Generators 7728k1 [0,-1,0,-8,-7440] 2 [29:126:1] 7728k2 [0,-1,0,-5768,-164112] 2 [-46:42:1]
7728l (4 curves)	1	2- 3+ 7- 23+	2- 3+ -2 7- -4  2  6  0
Curve Equation t Generators 7728l1 [0,-1,0,-9584,592320] 2 [-88:864:1] 7728l2 [0,-1,0,-178864,29166784] 4 [-120:6992:1] 7728l3 [0,-1,0,-204624,20243520] 2 [-134:6726:1] 7728l4 [0,-1,0,-2861584,1864147264] 4 [1338:20710:1]
7728m (1 curve)	1	2- 3+ 7- 23+	2- 3+  3 7- -4 -3 -4  0
Curve Equation t Generators 7728m1 [0,-1,0,145536,-14389248] 1 [4544:307328:1]
7728n (1 curve)	0	2- 3+ 7- 23-	2- 3+  4 7-  5 -2  0  5
Curve Equation t 7728n1 [0,-1,0,-1541,27693] 1
7728o (1 curve)	1	2- 3- 7+ 23+	2- 3-  1 7+  0 -1  4 -4
Curve Equation t Generators 7728o1 [0,1,0,-9840,373716] 1 [114:864:1]
7728p (2 curves)	1	2- 3- 7+ 23+	2- 3-  2 7+  4 -4 -4  2
Curve Equation t Generators 7728p1 [0,1,0,-235912,-54035212] 2 [1724:68310:1] 7728p2 [0,1,0,-4004232,-3085271820] 2 [4926:311040:1]
7728q (2 curves)	1	2- 3- 7+ 23+	2- 3- -4 7+ -2  2  2  2
Curve Equation t Generators 7728q1 [0,1,0,280,564] 2 [4:42:1] 7728q2 [0,1,0,-1160,3444] 2 [-20:138:1]
7728r (6 curves)	0	2- 3- 7+ 23-	2- 3- -2 7+  4 -2 -6 -4
Curve Equation t 7728r1 [0,1,0,2016,-70668] 2 7728r2 [0,1,0,-18464,-832524] 4 7728r3 [0,1,0,-283424,-58169868] 2 7728r4 [0,1,0,-81184,8073716] 8 7728r5 [0,1,0,-1266144,547941492] 4 7728r6 [0,1,0,100256,39208820] 4
7728s (1 curve)	0	2- 3- 7+ 23-	2- 3-  3 7+ -4  3  0  0
Curve Equation t 7728s1 [0,1,0,-82104,9072468] 1
7728t (1 curve)	1	2- 3- 7- 23-	2- 3-  0 7-  5 -6  4 -7
Curve Equation t Generators 7728t1 [0,1,0,-253,-7705] 1 [47:294:1]
7728u (2 curves)	1	2- 3- 7- 23-	2- 3- -2 7-  0  4  0 -6
Curve Equation t Generators 7728u1 [0,1,0,5336,-344908] 2 [92:966:1] 7728u2 [0,1,0,-53544,-4183884] 2 [-114:672:1]

Data from Elliptic Curve Data by J. E. Cremona.
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