Elliptic curve isogeny class 6.1-a over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-6.1-a
• Conductor: 6.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 6.1-a over \(\Q(\sqrt{105}) \)

Isogeny class 6.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
6.1-a1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -10 a - 130\) , \( -101 a - 917\bigr] \)
6.1-a2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
6.1-a3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5 a - 10\) , \( 4 a + 37\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph