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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-44800.5-g
• Conductor: 44800.5
• Rank: \( 1 \)

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

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

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

Isogeny class 44800.5-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
44800.5-g1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a + 7\) , \( -76 a - 312\bigr] \)
44800.5-g2	\( \bigl[0\) , \( a\) , \( 0\) , \( -85 a + 39\) , \( 172 a - 292\bigr] \)
44800.5-g3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -27 a + 162\) , \( -436 a - 36\bigr] \)
44800.5-g4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -427 a + 2562\) , \( -31556 a - 196\bigr] \)

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