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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
605.1-a1 605.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.730701665$ 1.307118876 \( \frac{145013028772769}{133974300625} a - \frac{234637911487596}{133974300625} \) \( \bigl[\phi + 1\) , \( \phi\) , \( 1\) , \( 4 \phi - 13\) , \( -1591 \phi - 1011\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(4\phi-13\right){x}-1591\phi-1011$
605.1-a2 605.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $23.38245330$ 1.307118876 \( -\frac{4826927}{605} a + \frac{8607801}{605} \) \( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( \phi - 1\) , \( -\phi + 2\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-1\right){x}-\phi+2$
605.1-a3 605.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $11.69122665$ 1.307118876 \( -\frac{54723249}{73205} a + \frac{252614698}{73205} \) \( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( \phi - 6\) , \( \phi - 2\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-6\right){x}+\phi-2$
605.1-a4 605.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.922806663$ 1.307118876 \( -\frac{1566703575423}{366025} a + \frac{511296585637}{73205} \) \( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( 36 \phi - 91\) , \( 147 \phi - 322\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(36\phi-91\right){x}+147\phi-322$
605.1-a5 605.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $5.845613327$ 1.307118876 \( \frac{857730789364547}{1071794405} a + \frac{530836755494779}{1071794405} \) \( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( -34 \phi - 1\) , \( 83 \phi + 2\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-34\phi-1\right){x}+83\phi+2$
605.1-a6 605.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.730701665$ 1.307118876 \( -\frac{25085621087436781}{605} a + \frac{40591422821635852}{605} \) \( \bigl[\phi\) , \( \phi - 1\) , \( 1\) , \( 586 \phi - 1466\) , \( 10927 \phi - 22432\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(586\phi-1466\right){x}+10927\phi-22432$
605.1-b1 605.1-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.730701665$ 1.307118876 \( -\frac{145013028772769}{133974300625} a - \frac{89624882714827}{133974300625} \) \( \bigl[\phi\) , \( \phi - 1\) , \( 0\) , \( -3 \phi - 10\) , \( 1581 \phi - 2595\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-3\phi-10\right){x}+1581\phi-2595$
605.1-b2 605.1-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $5.845613327$ 1.307118876 \( -\frac{857730789364547}{1071794405} a + \frac{1388567544859326}{1071794405} \) \( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( 35 \phi - 34\) , \( -84 \phi + 119\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(35\phi-34\right){x}-84\phi+119$
605.1-b3 605.1-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $11.69122665$ 1.307118876 \( \frac{54723249}{73205} a + \frac{197891449}{73205} \) \( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -4\) , \( -7 \phi - 2\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}-4{x}-7\phi-2$
605.1-b4 605.1-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $23.38245330$ 1.307118876 \( \frac{4826927}{605} a + \frac{3780874}{605} \) \( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+{x}$
605.1-b5 605.1-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.922806663$ 1.307118876 \( \frac{1566703575423}{366025} a + \frac{989779352762}{366025} \) \( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -35 \phi - 54\) , \( -238 \phi - 211\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-35\phi-54\right){x}-238\phi-211$
605.1-b6 605.1-b \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.730701665$ 1.307118876 \( \frac{25085621087436781}{605} a + \frac{15505801734199071}{605} \) \( \bigl[\phi + 1\) , \( \phi\) , \( 0\) , \( -585 \phi - 879\) , \( -12393 \phi - 12091\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-585\phi-879\right){x}-12393\phi-12091$
605.1-c1 605.1-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/2\Z$ $1.192245246$ $1.058161673$ 1.128398811 \( -\frac{649638087939825642}{1071794405} a + \frac{1051136507981046141}{1071794405} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( 48 \phi - 38\) , \( -1458 \phi - 1109\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(48\phi-38\right){x}-1458\phi-1109$
605.1-c2 605.1-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/4\Z$ $0.596122623$ $16.93058676$ 1.128398811 \( \frac{59319}{55} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$
605.1-c3 605.1-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.298061311$ $16.93058676$ 1.128398811 \( \frac{8120601}{3025} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$
605.1-c4 605.1-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.596122623$ $4.232646692$ 1.128398811 \( \frac{2749884201}{73205} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$
605.1-c5 605.1-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/4\Z$ $0.149030655$ $16.93058676$ 1.128398811 \( \frac{22930509321}{6875} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$
605.1-c6 605.1-c \(\Q(\sqrt{5}) \) \( 5 \cdot 11^{2} \) $1$ $\Z/2\Z$ $1.192245246$ $1.058161673$ 1.128398811 \( \frac{649638087939825642}{1071794405} a + \frac{401498420041220499}{1071794405} \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -48 \phi + 9\) , \( 1410 \phi - 2558\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-48\phi+9\right){x}+1410\phi-2558$
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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.