Elliptic curve isogeny class 252.1-c over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-252.1-c
• Conductor: 252.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 252.1-c over \(\Q(\sqrt{14}) \)

Isogeny class 252.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
252.1-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -13600 a - 50882\) , \( 1736782 a + 6498445\bigr] \)
252.1-c2	\( \bigl[0\) , \( a\) , \( 0\) , \( -800 a + 2998\) , \( -7126 a + 26665\bigr] \)
252.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -5\) , \( -3\bigr] \)
252.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -455\) , \( 3381\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph