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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-576.1-h
• 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-h over \(\Q(\sqrt{7}) \)

Isogeny class 576.1-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
576.1-h1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -42 a + 105\) , \( -94 a + 245\bigr] \)
576.1-h2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 38 a + 105\) , \( -14 a - 35\bigr] \)
576.1-h3	\( \bigl[0\) , \( a\) , \( 0\) , \( 120 a - 316\) , \( -1270 a + 3360\bigr] \)
576.1-h4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -101 a - 271\) , \( 849 a + 2247\bigr] \)
576.1-h5	\( \bigl[0\) , \( a\) , \( 0\) , \( -120 a - 316\) , \( -1270 a - 3360\bigr] \)
576.1-h6	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 99 a - 271\) , \( 1049 a - 2793\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph