Elliptic curve isogeny class 39375.1-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39375.1-d
• Conductor: 39375.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 39375.1-d over \(\Q(\sqrt{-7}) \)

Isogeny class 39375.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
39375.1-d1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -850\) , \( -27125\bigr] \)
39375.1-d2	\( \bigl[1\) , \( 1\) , \( 0\) , \( 25\) , \( 0\bigr] \)
39375.1-d3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -100\) , \( -125\bigr] \)
39375.1-d4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -51 a + 41\) , \( 49 a - 246\bigr] \)
39375.1-d5	\( \bigl[1\) , \( 1\) , \( 0\) , \( -975\) , \( 11250\bigr] \)
39375.1-d6	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 50 a - 10\) , \( -50 a - 197\bigr] \)
39375.1-d7	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1225\) , \( -17000\bigr] \)
39375.1-d8	\( \bigl[1\) , \( 1\) , \( 0\) , \( -19600\) , \( -1064375\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 16 & 8 & 16 & 2 & 4 \\ 8 & 1 & 2 & 2 & 4 & 2 & 4 & 8 \\ 4 & 2 & 1 & 4 & 2 & 4 & 2 & 4 \\ 16 & 2 & 4 & 1 & 8 & 4 & 8 & 16 \\ 8 & 4 & 2 & 8 & 1 & 8 & 4 & 8 \\ 16 & 2 & 4 & 4 & 8 & 1 & 8 & 16 \\ 2 & 4 & 2 & 8 & 4 & 8 & 1 & 2 \\ 4 & 8 & 4 & 16 & 8 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph