Elliptic curve isogeny class 72.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-72.1-a
• Conductor: 72.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 72.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 72.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
72.1-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -473 a + 1763\) , \( 77252 a - 289054\bigr] \)
72.1-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 127 a - 482\) , \( -811 a + 3031\bigr] \)
72.1-a4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -727 a - 2727\) , \( -21814 a - 81624\bigr] \)
72.1-a5	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1927 a - 7217\) , \( -83968 a + 314176\bigr] \)
72.1-a6	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 11527 a - 43137\) , \( 1335256 a - 4996074\bigr] \)

Rank

Rank: \( 0 \)

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