Elliptic curve isogeny class 196.1-b over number field \(\Q(\sqrt{93}) \)

• Base field: \(\Q(\sqrt{93}) \)
• Label: 2.2.93.1-196.1-b
• Conductor: 196.1
• Rank bounds: 0...1

Base field \(\Q(\sqrt{93}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 23 \); class number \(1\).

Elliptic curves in class 196.1-b over \(\Q(\sqrt{93}) \)

Isogeny class 196.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
196.1-b1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -14839 a - 64112\) , \( 2157342 a + 9323679\bigr] \)
196.1-b2	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -49 a - 192\) , \( -768 a - 3295\bigr] \)
196.1-b3	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 386 a + 1688\) , \( 15657 a + 67691\bigr] \)
196.1-b4	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3094 a - 13352\) , \( 166497 a + 719595\bigr] \)
196.1-b5	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 917 a - 4870\) , \( 33617 a - 178884\bigr] \)
196.1-b6	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -237559 a - 1026672\) , \( 138254622 a + 597512351\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph