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

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-5.1-c
• Conductor: 5.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
5.1-c1	\( \bigl[1\) , \( -1\) , \( a\) , \( 2623 a - 14753\) , \( 164908 a - 927364\bigr] \)
5.1-c2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 7164 a - 40283\) , \( -508682 a + 2860562\bigr] \)
5.1-c3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 2649 a - 14893\) , \( 171401 a - 963868\bigr] \)
5.1-c4	\( \bigl[1\) , \( -1\) , \( a\) , \( -a - 1\) , \( -10\bigr] \)

Rank

Rank: \( 0 \)

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