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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
10.1-a1 10.1-a 3.3.733.1 \( 2 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $126.0013261$ 2.326982585 \( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \) \( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a\) , \( -254283425430303815 a^{2} - 386052765748533969 a + 807826405432831715\) , \( -128265428101555296555965052 a^{2} - 194732406112317607687625258 a + 407483104922159986550542545\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-254283425430303815a^{2}-386052765748533969a+807826405432831715\right){x}-128265428101555296555965052a^{2}-194732406112317607687625258a+407483104922159986550542545$
50.2-c5 50.2-c 3.3.733.1 \( 2 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $44.91956525$ 1.659141999 \( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \) \( \bigl[a + 1\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( -78197826161174 a^{2} - 118719837968040 a + 248424641572868\) , \( -691710806524498198688 a^{2} - 1050154446775467734780 a + 2197478083709730946512\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-78197826161174a^{2}-118719837968040a+248424641572868\right){x}-691710806524498198688a^{2}-1050154446775467734780a+2197478083709730946512$
80.3-a5 80.3-a 3.3.733.1 \( 2^{4} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.653147090$ $26.86943903$ 3.949655339 \( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \) \( \bigl[a\) , \( a^{2} - 4\) , \( a^{2} + a - 4\) , \( -24503 a^{2} - 37200 a + 77845\) , \( -3868666 a^{2} - 5873399 a + 12290258\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-24503a^{2}-37200a+77845\right){x}-3868666a^{2}-5873399a+12290258$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.