Elliptic curve isogeny class 98.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-98.1-a
• Conductor: 98.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 98.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 98.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
98.1-a1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 4773 a - 17896\) , \( 359516 a - 1345126\bigr] \)
98.1-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 13 a - 46\) , \( -88 a + 330\bigr] \)
98.1-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -127 a + 479\) , \( 2208 a - 8259\bigr] \)
98.1-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 993 a - 3721\) , \( 29312 a - 109675\bigr] \)
98.1-a5	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 293 a - 1096\) , \( -4680 a + 17508\bigr] \)
98.1-a6	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 76453 a - 286696\) , \( 22465628 a - 84053094\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph