Elliptic curve isogeny class 144.1-e over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-144.1-e
• Conductor: 144.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 144.1-e over \(\Q(\sqrt{7}) \)

Isogeny class 144.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
144.1-e1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 6\) , \( -2 a + 4\bigr] \)
144.1-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 270 a - 714\) , \( 4014 a - 10620\bigr] \)
144.1-e3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a - 6\) , \( 2 a + 4\bigr] \)
144.1-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -270 a - 714\) , \( -4014 a - 10620\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph