Elliptic curve isogeny class 10.2-c over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-10.2-c
• Conductor: 10.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 10.2-c over \(\Q(\sqrt{14}) \)

Isogeny class 10.2-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
10.2-c1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1285 a - 4941\) , \( 48650 a + 182431\bigr] \)
10.2-c2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 5 a + 29\) , \( 20 a + 81\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph