Properties

Base field \(\Q(\sqrt{15}) \)
Label 2.2.60.1-75.1-b
Conductor 75.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 75.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 75.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
75.1-b1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -266 a - 1028\) , \( 5216 a + 20202\bigr] \)
75.1-b2 \( \bigl[0\) , \( -1\) , \( a\) , \( 2\) , \( -8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph