Elliptic curve isogeny class 100.1-a over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-100.1-a
• Conductor: 100.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{37}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 9 \); class number \(1\).

Elliptic curves in class 100.1-a over \(\Q(\sqrt{37}) \)

Isogeny class 100.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100.1-a1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -1307 a - 3321\) , \( -75912 a - 192922\bigr] \)
100.1-a2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -1547 a - 3931\) , \( -57330 a - 145698\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph