Elliptic curve isogeny class 64.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-64.1-b
• Conductor: 64.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 64.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 64.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
64.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
64.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a + 127\) , \( 0\bigr] \)
64.1-b3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 134 a - 345\) , \( 1298 a - 3425\bigr] \)
64.1-b4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 135 a - 341\) , \( -1379 a + 3661\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph