Elliptic curve isogeny class 27.1-b over number field \(\Q(\sqrt{205}) \)

• Base field: \(\Q(\sqrt{205}) \)
• Label: 2.2.205.1-27.1-b
• Conductor: 27.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{205}) \)

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

Elliptic curves in class 27.1-b over \(\Q(\sqrt{205}) \)

Isogeny class 27.1-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[0\) , \( a\) , \( 1\) , \( 19 a - 129\) , \( 394 a - 3011\bigr] \)
27.1-b2	\( \bigl[0\) , \( a\) , \( 1\) , \( -81 a - 519\) , \( -1762 a - 11739\bigr] \)
27.1-b3	\( \bigl[0\) , \( 0\) , \( 1\) , \( -168 a - 1146\) , \( 11732 a + 78177\bigr] \)
27.1-b4	\( \bigl[0\) , \( a\) , \( 1\) , \( 19 a + 141\) , \( -356 a - 2381\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph