Elliptic curve isogeny class 126.1-e over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-126.1-e
• Conductor: 126.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 126.1-e over \(\Q(\sqrt{7}) \)

Isogeny class 126.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
126.1-e1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 24 a - 61\) , \( 87 a - 229\bigr] \)
126.1-e2	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -171 a + 454\) , \( -1361 a + 3601\bigr] \)
126.1-e3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 54 a - 141\) , \( -239 a + 633\bigr] \)
126.1-e4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 759 a - 2016\) , \( -19061 a + 50433\bigr] \)

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