Elliptic curve isogeny class 100.1-d over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-100.1-d
• Conductor: 100.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.1-d over \(\Q(\sqrt{7}) \)

Isogeny class 100.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-d1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -435 a - 1148\) , \( -12954 a - 34274\bigr] \)
100.1-d2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 45 a + 122\) , \( 336 a + 888\bigr] \)
100.1-d3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.1-d4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph