Elliptic curve isogeny class 289.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-289.1-b
• Conductor: 289.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

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

Elliptic curves in class 289.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 289.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
289.1-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( -4\) , \( 12\bigr] \)
289.1-b2	\( \bigl[a\) , \( -1\) , \( a\) , \( -4\) , \( -2\bigr] \)
289.1-b3	\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( 2\bigr] \)
289.1-b4	\( \bigl[a\) , \( -1\) , \( a\) , \( -94\) , \( 308\bigr] \)