Elliptic curve isogeny class 15.1-a over number field \(\Q(\sqrt{301}) \)

• Base field: \(\Q(\sqrt{301}) \)
• Label: 2.2.301.1-15.1-a
• Conductor: 15.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{301}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 75 \); class number \(1\).

Elliptic curves in class 15.1-a over \(\Q(\sqrt{301}) \)

Isogeny class 15.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
15.1-a1	\( \bigl[0\) , \( -1\) , \( 1\) , \( -1910572 a + 17528879\) , \( 2687078497 a - 24653074023\bigr] \)
15.1-a2	\( \bigl[0\) , \( -1\) , \( 1\) , \( 90938 a + 743389\) , \( 84627209 a + 691799996\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph