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Results (6 matches)

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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
15.1-a2 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.156163233$ 0.889910366 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 174 a + 260\) , \( 145 a + 374\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(174a+260\right){x}+145a+374$
15.1-b2 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.220649536$ 1.065470266 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 275 a - 734\) , \( 3747 a - 10492\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(275a-734\right){x}+3747a-10492$
45.2-a2 45.2-a \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.738807389$ 1.289767919 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 2347 a + 4171\) , \( 20528 a + 36708\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(2347a+4171\right){x}+20528a+36708$
45.2-b2 45.2-b \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.320973547$ $4.491841405$ 1.258473281 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 273 a - 279\) , \( -1724 a + 5275\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(273a-279\right){x}-1724a+5275$
1875.1-k2 1875.1-k \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.880738313$ $1.631232646$ 5.525614808 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4359 a + 6472\) , \( 39901 a + 90526\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4359a+6472\right){x}+39901a+90526$
1875.1-bj2 1875.1-bj \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.244129907$ 1.704752426 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( 6872 a - 18375\) , \( 456884 a - 1277134\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(6872a-18375\right){x}+456884a-1277134$
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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.