Elliptic curve isogeny class 5.1-a over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-5.1-a
• Conductor: 5.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 5.1-a over \(\Q(\sqrt{105}) \)

Isogeny class 5.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5.1-a1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 101 a + 507\) , \( 12625 a + 58420\bigr] \)
5.1-a2	\( \bigl[1\) , \( -1\) , \( a\) , \( -426911 a - 1973810\) , \( -245763021 a - 1136279283\bigr] \)
5.1-a3	\( \bigl[1\) , \( -1\) , \( a\) , \( -157991 a - 730465\) , \( 74372212 a + 343858086\bigr] \)
5.1-a4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2500155 a - 11559365\) , \( 4867995135 a + 22507055720\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph