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

• Base field: \(\Q(\sqrt{51}) \)
• Label: 2.2.204.1-36.1-b
• 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-b over \(\Q(\sqrt{51}) \)

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

Curve label	Weierstrass Coefficients
36.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -27\bigr] \)
36.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)
36.1-b3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 23636 a - 168656\) , \( 5207152 a - 37186086\bigr] \)
36.1-b4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2636 a - 18686\) , \( -191324 a + 1366744\bigr] \)

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