Elliptic curve isogeny class 36.1-a over number field \(\Q(\sqrt{51}) \)

• Base field: \(\Q(\sqrt{51}) \)
• Label: 2.2.204.1-36.1-a
• Conductor: 36.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{51}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 51 \); class number \(2\).

Elliptic curves in class 36.1-a over \(\Q(\sqrt{51}) \)

Isogeny class 36.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \)
36.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \)
36.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2637 a - 18660\) , \( 193638 a - 1382418\bigr] \)
36.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 23637 a - 168630\) , \( -5186808 a + 37041652\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph