Elliptic curve isogeny class 39204.4-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.4-d
• Conductor: 39204.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 39204.4-d over \(\Q(\sqrt{-7}) \)

Isogeny class 39204.4-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
39204.4-d1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 2434 a - 6521\) , \( -104412 a + 182117\bigr] \)
39204.4-d2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -932 a - 746\) , \( -14179 a + 9197\bigr] \)
39204.4-d3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 2308 a + 4294\) , \( -110875 a + 48509\bigr] \)
39204.4-d4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2354 a + 2245\) , \( -15978 a + 76471\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph