Elliptic curve isogeny class 28672.5-l over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28672.5-l
• Conductor: 28672.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 28672.5-l over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.5-l contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
28672.5-l1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 19 a + 7\) , \( 3 a + 67\bigr] \)
28672.5-l2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -221 a - 313\) , \( 2723 a + 1155\bigr] \)
28672.5-l3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 5 a + 15\bigr] \)
28672.5-l4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 242 a - 153\) , \( -747 a - 1617\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph