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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4.1-a2 4.1-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $7.662151750$ 1.014876791 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -71396 a - 233865\) , \( 20071185 a + 65731670\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-71396a-233865\right){x}+20071185a+65731670$
4.1-d2 4.1-d \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.077866687$ 1.516113114 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 642628 a - 2747187\) , \( 545795628 a - 2333231135\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(642628a-2747187\right){x}+545795628a-2333231135$
36.1-b2 36.1-b \(\Q(\sqrt{57}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/3\Z$ $1$ $0.772415932$ 1.671046829 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 5674 a - 29613\) , \( -560830 a + 2247997\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(5674a-29613\right){x}-560830a+2247997$
36.1-f2 36.1-f \(\Q(\sqrt{57}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.257471977$ 1.671046829 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -64690451 a - 211855871\) , \( 550295059293 a + 1802170764457\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-64690451a-211855871\right){x}+550295059293a+1802170764457$
128.5-c2 128.5-c \(\Q(\sqrt{57}) \) \( 2^{7} \) $0$ $\mathsf{trivial}$ $1$ $0.157668741$ 6.139818101 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -2811454 a - 9207370\) , \( 4982304576 a + 16316634679\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2811454a-9207370\right){x}+4982304576a+16316634679$
128.5-j2 128.5-j \(\Q(\sqrt{57}) \) \( 2^{7} \) $1$ $\mathsf{trivial}$ $3.301024792$ $0.473006225$ 1.654505450 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 1044512 a - 4465409\) , \( -1129233268 a + 4827376713\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1044512a-4465409\right){x}-1129233268a+4827376713$
128.6-c2 128.6-c \(\Q(\sqrt{57}) \) \( 2^{7} \) $0$ $\mathsf{trivial}$ $1$ $0.473006225$ 6.139818101 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -115777 a - 381257\) , \( -42294261 a - 138472621\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-115777a-381257\right){x}-42294261a-138472621$
128.6-j2 128.6-j \(\Q(\sqrt{57}) \) \( 2^{7} \) $1$ $\mathsf{trivial}$ $9.903074376$ $0.157668741$ 1.654505450 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 25303280 a - 108169436\) , \( 134641581530 a - 575581615086\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25303280a-108169436\right){x}+134641581530a-575581615086$
256.1-a2 256.1-a \(\Q(\sqrt{57}) \) \( 2^{8} \) $0$ $\mathsf{trivial}$ $1$ $1.915537937$ 4.059507167 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10282065 a - 43955062\) , \( -34876683146 a + 149094933468\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10282065a-43955062\right){x}-34876683146a+149094933468$
256.1-r2 256.1-r \(\Q(\sqrt{57}) \) \( 2^{8} \) $0$ $\mathsf{trivial}$ $1$ $0.019466671$ 0.505371038 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1142335 a - 3741902\) , \( -1289440094 a - 4222819768\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1142335a-3741902\right){x}-1289440094a-4222819768$
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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.