Elliptic curve isogeny class 32.1-a over number field \(\Q(\sqrt{62}) \)

• Base field: \(\Q(\sqrt{62}) \)
• Label: 2.2.248.1-32.1-a
• Conductor: 32.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{62}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 62 \); class number \(1\).

Elliptic curves in class 32.1-a over \(\Q(\sqrt{62}) \)

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

Curve label	Weierstrass Coefficients
32.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1008 a - 7937\) , \( 0\bigr] \)
32.1-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( 57\) , \( 134\bigr] \)
32.1-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 88\) , \( 153\bigr] \)

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