Elliptic curve isogeny class 576.2-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-576.2-a
• Conductor: 576.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 576.2-a over \(\Q(\sqrt{7}) \)

Isogeny class 576.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.2-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 11\) , \( 0\bigr] \)
576.2-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -20 a - 53\) , \( 0\bigr] \)
576.2-a3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 14 a - 22\) , \( -35 a + 102\bigr] \)
576.2-a4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 13 a - 26\) , \( 31 a - 75\bigr] \)

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