Elliptic curve isogeny class 200.1-e over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-200.1-e
• Conductor: 200.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 200.1-e over \(\Q(\sqrt{7}) \)

Isogeny class 200.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
200.1-e1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 159 a + 421\) , \( 3616 a + 9567\bigr] \)
200.1-e2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -81 a - 214\) , \( 381 a + 1008\bigr] \)
200.1-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
200.1-e4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 1286 a - 3393\) , \( -41149 a + 108879\bigr] \)

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