Elliptic curve isogeny class 2709.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-2709.1-a
• Conductor: 2709.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2709.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 2709.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2709.1-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -856 a + 715\) , \( -5026 a + 16702\bigr] \)
2709.1-a2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 288 a - 659\) , \( -8353 a + 3413\bigr] \)
2709.1-a3	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 18 a + 286\) , \( -1252 a + 1199\bigr] \)
2709.1-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 214 a + 60\) , \( -174 a + 2317\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph