Elliptic curve isogeny class 18.2-a over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-18.2-a
• Conductor: 18.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 18.2-a over \(\Q(\sqrt{7}) \)

Isogeny class 18.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
18.2-a1	\( \bigl[a\) , \( -a\) , \( 1\) , \( -6 a - 8\) , \( 34 a + 93\bigr] \)
18.2-a2	\( \bigl[a\) , \( -a\) , \( a\) , \( 74 a - 199\) , \( 691 a - 1830\bigr] \)
18.2-a3	\( \bigl[a\) , \( -a\) , \( a\) , \( 1204 a - 3189\) , \( 38811 a - 102686\bigr] \)
18.2-a4	\( \bigl[a\) , \( -a\) , \( 1\) , \( -121 a - 313\) , \( 1188 a + 3145\bigr] \)

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