Elliptic curve isogeny class 9.1-c over number field \(\Q(\sqrt{145}) \)

• Base field: \(\Q(\sqrt{145}) \)
• Label: 2.2.145.1-9.1-c
• Number of curves: 6
• Conductor: 9.1
• Rank: \( 2 \)

Base field \(\Q(\sqrt{145}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 36 \); class number \(4\).

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 9.1-c over \(\Q(\sqrt{145}) \)

Isogeny class 9.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9.1-c1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 22 a - 95\) , \( -57 a + 488\bigr] \)
9.1-c2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 128675 a - 839063\) , \( 61701250 a - 402341344\bigr] \)
9.1-c3	\( \bigl[1\) , \( 1\) , \( 1\) , \( 8425 a - 54938\) , \( 870000 a - 5673094\bigr] \)
9.1-c4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 2425 a - 15813\) , \( -145750 a + 950406\bigr] \)
9.1-c5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -15825 a + 103187\) , \( 4926750 a - 32126344\bigr] \)
9.1-c6	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -22 a - 72\) , \( 79 a + 504\bigr] \)