Elliptic curve isogeny class 20.1-c over number field \(\Q(\sqrt{35}) \)

• Base field: \(\Q(\sqrt{35}) \)
• Label: 2.2.140.1-20.1-c
• Conductor: 20.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{35}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 35 \); class number \(2\).

Elliptic curves in class 20.1-c over \(\Q(\sqrt{35}) \)

Isogeny class 20.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20.1-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \)
20.1-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \)
20.1-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
20.1-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph