Elliptic curve isogeny class 24.1-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-24.1-a
• Conductor: 24.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 24.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 24.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
24.1-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6 a + 16\) , \( 0\bigr] \)
24.1-a2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 194 a - 514\) , \( -2156 a + 5704\bigr] \)
24.1-a3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 24 a - 64\) , \( 80 a - 212\bigr] \)
24.1-a4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 334 a - 894\) , \( 5836 a - 15456\bigr] \)

Rank

Rank: \( 0 \)

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