Elliptic curve isogeny class 98.1-g over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-98.1-g
• Conductor: 98.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 23 \); class number \(1\).

Elliptic curves in class 98.1-g over \(\Q(\sqrt{23}) \)

Isogeny class 98.1-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
98.1-g1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
98.1-g2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 38 a - 188\bigr] \)
98.1-g3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 517 a - 2501\) , \( 16248 a - 77950\bigr] \)
98.1-g4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 27 a - 151\) , \( 340 a - 1658\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph