Elliptic curve isogeny class 18.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-18.1-a
• Conductor: 18.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 18.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 18.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
18.1-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2\) , \( -38 a - 142\bigr] \)
18.1-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -80 a - 298\) , \( -738 a - 2762\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph