Elliptic curve isogeny class 44800.5-l over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-44800.5-l
• Conductor: 44800.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 44800.5-l over \(\Q(\sqrt{-7}) \)

Isogeny class 44800.5-l contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
44800.5-l1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 57 a + 1914\) , \( 27314 a - 22200\bigr] \)
44800.5-l2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 536 a + 1120\) , \( 21632 a - 26860\bigr] \)
44800.5-l3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a - 166\) , \( -126 a + 616\bigr] \)
44800.5-l4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -30264 a + 23520\) , \( 1086752 a - 3364460\bigr] \)
44800.5-l5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 456 a - 320\) , \( 3872 a + 1108\bigr] \)
44800.5-l6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10057 a + 157914\) , \( 19030114 a - 12691800\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 6 & 3 \\ 2 & 1 & 6 & 3 & 3 & 6 \\ 3 & 6 & 1 & 18 & 2 & 9 \\ 6 & 3 & 18 & 1 & 9 & 2 \\ 6 & 3 & 2 & 9 & 1 & 18 \\ 3 & 6 & 9 & 2 & 18 & 1 \end{array}\right)\)

Isogeny graph