Elliptic curve isogeny class 32.1-e over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-32.1-e
• Conductor: 32.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 32.1-e over \(\Q(\sqrt{14}) \)

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

Curve label	Weierstrass Coefficients
32.1-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a - 449\) , \( 0\bigr] \)
32.1-e3	\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -6\bigr] \)
32.1-e4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( 1\bigr] \)

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