Elliptic curve isogeny class 72.1-c over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-72.1-c
• Conductor: 72.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 72.1-c over \(\Q(\sqrt{14}) \)

Isogeny class 72.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
72.1-c1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 8\) , \( 28\bigr] \)
72.1-c2	\( \bigl[0\) , \( a\) , \( 0\) , \( 80 a + 304\) , \( -832 a - 3115\bigr] \)
72.1-c3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \)
72.1-c4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \)
72.1-c5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -12\) , \( -42\bigr] \)
72.1-c6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -92\) , \( 252\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph