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Results (13 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
75.1-a6 75.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.117850856$ 0.322695746 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
1875.1-b6 1875.1-b \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.223570171$ 1.032626388 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$
11025.1-c6 11025.1-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.243935055$ 2.253375518 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 2025 a + 1215\) , \( -37159 a + 66759\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2025a+1215\right){x}-37159a+66759$
11025.3-c6 11025.3-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.243935055$ 2.253375518 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1213 a - 2026\) , \( 33919 a + 30815\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1213a-2026\right){x}+33919a+30815$
12675.1-a6 12675.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.310036044$ 2.863990301 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -1079 a + 2025\) , \( -21863 a - 9057\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1079a+2025\right){x}-21863a-9057$
12675.3-a6 12675.3-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.310036044$ 2.863990301 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2025 a + 1081\) , \( 22808 a - 32945\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2025a+1081\right){x}+22808a-32945$
19200.1-g6 19200.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $2.600625687$ $0.279462714$ 3.356843389 \( \frac{272223782641}{164025} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -2160\) , \( 37908\bigr] \) ${y}^2={x}^{3}+{x}^{2}-2160{x}+37908$
57600.1-j6 57600.1-j \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $5.329321481$ $0.161347873$ 3.971591054 \( \frac{272223782641}{164025} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6480 a\) , \( -227448 a + 113724\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-6480a{x}-227448a+113724$
57600.1-k6 57600.1-k \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $5.329321481$ $0.161347873$ 3.971591054 \( \frac{272223782641}{164025} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6482 a - 6481\) , \( 233929 a - 120205\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6482a-6481\right){x}+233929a-120205$
81225.1-a6 81225.1-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.027707458$ $0.148062962$ 2.754442525 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -2026 a - 6481\) , \( -104775 a - 192360\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2026a-6481\right){x}-104775a-192360$
81225.3-a6 81225.3-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.027707458$ $0.148062962$ 2.754442525 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( a\) , \( a\) , \( 6481 a + 2025\) , \( 104774 a - 297134\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6481a+2025\right){x}+104774a-297134$
102675.1-a6 102675.1-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 37^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $12.07263470$ $0.183773548$ 5.123708641 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 945 a + 4456\) , \( 151963 a - 107681\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(945a+4456\right){x}+151963a-107681$
102675.3-a6 102675.3-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 37^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $12.07263470$ $0.183773548$ 5.123708641 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 5401 a - 4456\) , \( -151963 a + 44282\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(5401a-4456\right){x}-151963a+44282$
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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.