Elliptic curve isogeny class 9.2-c over number field \(\Q(\sqrt{301}) \)

• Base field: \(\Q(\sqrt{301}) \)
• Label: 2.2.301.1-9.2-c
• Conductor: 9.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{301}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 75 \); class number \(1\).

Elliptic curves in class 9.2-c over \(\Q(\sqrt{301}) \)

Isogeny class 9.2-c contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
9.2-c1	\( \bigl[1\) , \( -1\) , \( a\) , \( -13 a - 102\) , \( 90 a + 719\bigr] \)
9.2-c2	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 120854 a - 1108595\) , \( 83293389 a - 764189269\bigr] \)
9.2-c3	\( \bigl[1\) , \( -1\) , \( a\) , \( -213 a - 1737\) , \( 5019 a + 41012\bigr] \)
9.2-c4	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 2054379 a - 18848060\) , \( 4728597369 a - 43383347215\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph