Elliptic curve isogeny class 1521.3-j over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.3-j
• Conductor: 1521.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 1521.3-j over \(\Q(\sqrt{13}) \)

Isogeny class 1521.3-j contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
1521.3-j1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1325 a - 5743\) , \( -132890 a - 16526\bigr] \)
1521.3-j2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 40 a - 88\) , \( 178 a - 419\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph