Elliptic curve isogeny class 50.1-e over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-50.1-e
• Conductor: 50.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 50.1-e over \(\Q(\sqrt{14}) \)

Isogeny class 50.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
50.1-e1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -42 a - 149\) , \( -333 a - 1243\bigr] \)
50.1-e2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -702 a - 2709\) , \( -17141 a - 63939\bigr] \)
50.1-e3	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -682 a - 2549\) , \( -18925 a - 70811\bigr] \)
50.1-e4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -10902 a - 40789\) , \( -1201637 a - 4496115\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph