Elliptic curve isogeny class 72.1-h over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-72.1-h
• Conductor: 72.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 72.1-h over \(\Q(\sqrt{23}) \)

Isogeny class 72.1-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
72.1-h1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -938 a + 4522\) , \( -252644 a + 1211660\bigr] \)
72.1-h2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-h3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 262 a - 1233\) , \( 4046 a - 19382\bigr] \)
72.1-h4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1462 a - 6988\) , \( -61684 a + 295848\bigr] \)
72.1-h5	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3862 a - 18498\) , \( 290486 a - 1393100\bigr] \)
72.1-h6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -23062 a - 110578\) , \( 4146604 a + 19886436\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph