Elliptic curve isogeny class 32.1-c over number field \(\Q(\sqrt{46}) \)

• Base field: \(\Q(\sqrt{46}) \)
• Label: 2.2.184.1-32.1-c
• Conductor: 32.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{46}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 46 \); class number \(1\).

Elliptic curves in class 32.1-c over \(\Q(\sqrt{46}) \)

Isogeny class 32.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
32.1-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-c2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -174627960 a - 1184384449\) , \( 0\bigr] \)
32.1-c3	\( \bigl[a\) , \( -1\) , \( a\) , \( 11\) , \( 20\bigr] \)
32.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 34\) , \( 35\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph