Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 2 a + 10\) , \( 2 a + 7\bigr] \)
1.1-a2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4 a + 3\) , \( a + 21\bigr] \)
1.1-a3	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -18 a - 65\) , \( 41 a + 153\bigr] \)
1.1-a4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 24 a - 72\) , \( -113 a + 447\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph