Elliptic curve isogeny class 576.1-f over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-576.1-f
• Conductor: 576.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 576.1-f over \(\Q(\sqrt{7}) \)

Isogeny class 576.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.1-f1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -91 a + 249\) , \( -425 a + 1129\bigr] \)
576.1-f2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
576.1-f3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -208 a - 550\) , \( -2676 a - 7080\bigr] \)
576.1-f4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 388 a - 1025\) , \( -7148 a + 18913\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph