Elliptic curve isogeny class 9.3-b over number field \(\Q(\sqrt{67}) \)

• Base field: \(\Q(\sqrt{67}) \)
• Label: 2.2.268.1-9.3-b
• Conductor: 9.3
• Rank bounds: 0...1

Base field \(\Q(\sqrt{67}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 67 \); class number \(1\).

Elliptic curves in class 9.3-b over \(\Q(\sqrt{67}) \)

Isogeny class 9.3-b contains 2 curves linked by isogenies of degree 67.

Curve label	Weierstrass Coefficients
9.3-b1	\( \bigl[0\) , \( 0\) , \( a\) , \( 1760 a - 14410\) , \( 115010 a - 941417\bigr] \)
9.3-b2	\( \bigl[0\) , \( 0\) , \( 1\) , \( 1760 a - 14410\) , \( -115010 a + 941400\bigr] \)

Rank

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

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 67 \\ 67 & 1 \end{array}\right)\)

Isogeny graph