Elliptic curve isogeny class 26244.2-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-26244.2-b
• Conductor: 26244.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 26244.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 26244.2-b contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
26244.2-b1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1077\) , \( 13877\bigr] \)
26244.2-b2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -42\) , \( -100\bigr] \)
26244.2-b3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -852\) , \( 19664\bigr] \)
26244.2-b4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph