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Results (10 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
78400.2-a1 78400.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $0.011277526$ $0.457060343$ 2.142689697 \( -\frac{30211716096}{1071875} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -412\) , \( 3316\bigr] \) ${y}^2={x}^{3}-412{x}+3316$
78400.2-b1 78400.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.691494724$ 1.596938661 \( \frac{10678754}{30625} a + \frac{30044446}{30625} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a + 58\) , \( 41 a + 201\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(43a+58\right){x}+41a+201$
78400.2-b2 78400.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.382989449$ 1.596938661 \( -\frac{24375452}{175} a + 17568 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a + 58\) , \( 185 a - 111\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(3a+58\right){x}+185a-111$
78400.2-c1 78400.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.382989449$ 1.596938661 \( \frac{24375452}{175} a - \frac{21301052}{175} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 61 a - 58\) , \( -185 a + 74\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(61a-58\right){x}-185a+74$
78400.2-c2 78400.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.691494724$ 1.596938661 \( -\frac{10678754}{30625} a + \frac{232704}{175} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 101 a - 58\) , \( -41 a + 242\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(101a-58\right){x}-41a+242$
78400.2-d1 78400.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $0.097431715$ $3.073025053$ 2.765832067 \( -\frac{1024}{35} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 5\bigr] \) ${y}^2={x}^{3}-{x}^{2}-{x}+5$
78400.2-e1 78400.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.278521437$ 3.216088539 \( \frac{5265266308346}{1412376245} a - \frac{159677937425154}{7061881225} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -128 a - 976\) , \( -2944 a - 12020\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-128a-976\right){x}-2944a-12020$
78400.2-e2 78400.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.557042875$ 3.216088539 \( \frac{1920508084}{2100875} a - \frac{7387021088}{10504375} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -128 a + 24\) , \( 656 a - 820\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-128a+24\right){x}+656a-820$
78400.2-f1 78400.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.278521437$ 3.216088539 \( -\frac{5265266308346}{1412376245} a - \frac{133351605883424}{7061881225} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -1104 a + 976\) , \( 2944 a - 14964\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-1104a+976\right){x}+2944a-14964$
78400.2-f2 78400.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.557042875$ 3.216088539 \( -\frac{1920508084}{2100875} a + \frac{2215519332}{10504375} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -104 a - 24\) , \( -656 a - 164\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-104a-24\right){x}-656a-164$
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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.