Elliptic curve isogeny class 27.3-a over number field \(\Q(\sqrt{-14}) \)

• Base field: \(\Q(\sqrt{-14}) \)
• Label: 2.0.56.1-27.3-a
• Conductor: 27.3
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} + 14 \); class number \(4\).

Elliptic curves in class 27.3-a over \(\Q(\sqrt{-14}) \)

Isogeny class 27.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
27.3-a1	\( \bigl[a\) , \( -a\) , \( 1\) , \( -4 a - 16\) , \( -3 a - 13\bigr] \)
27.3-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 52 a - 125\) , \( -460 a + 407\bigr] \)
27.3-a3	\( \bigl[a\) , \( -a\) , \( 1\) , \( 11 a + 44\) , \( -100 a - 62\bigr] \)
27.3-a4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 26\) , \( -14 a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph