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Base field Conductor norm Rank* Torsion order CM discriminant
Base field degree/signature Bad \(p\) $\Q$-curves Torsion structure CM
Analytic order of Ш* Cyclic isogeny degree Isogeny class size Reduction Galois image
j-invariant Regulator* Curves per isogeny class Isogeny class degree Nonmax$\ \ell$
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Results (8 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
64.1-a1 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.490374880$ 1.52868 \( -\frac{1250637664527933}{32} a^{4} + \frac{1250637664527933}{32} a^{3} + \frac{1250637664527933}{8} a^{2} - \frac{1250637664527933}{16} a - \frac{2690606637259811}{16} \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -29 a^{4} + 28 a^{3} + 116 a^{2} - 56 a - 85\) , \( -53 a^{4} + 51 a^{3} + 211 a^{2} - 102 a - 263\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+{x}^{2}+\left(-29a^{4}+28a^{3}+116a^{2}-56a-85\right){x}-53a^{4}+51a^{3}+211a^{2}-102a-263$
64.1-a2 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23287.10750$ 1.52868 \( -\frac{461373}{2} a^{4} + \frac{461373}{2} a^{3} + 922746 a^{2} - 461373 a - 992771 \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( -2 a^{4} + a^{3} + 8 a^{2} - 2 a - 7\) , \( -a^{3} - a^{2} + 2 a + 2\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){y}={x}^{3}+{x}^{2}+\left(-2a^{4}+a^{3}+8a^{2}-2a-7\right){x}-a^{3}-a^{2}+2a+2$
64.1-a3 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.490374880$ 1.52868 \( -\frac{1680914269}{32768} \) \( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( -a^{5} + a^{4} + 4 a^{3} - 4 a^{2} - 2 a + 1\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( 297 a^{5} - 225 a^{4} - 1336 a^{3} + 923 a^{2} + 1137 a - 917\) , \( 4026 a^{5} - 3233 a^{4} - 18380 a^{3} + 13142 a^{2} + 16483 a - 12186\bigr] \) ${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-4a^{2}-2a+1\right){x}^{2}+\left(297a^{5}-225a^{4}-1336a^{3}+923a^{2}+1137a-917\right){x}+4026a^{5}-3233a^{4}-18380a^{3}+13142a^{2}+16483a-12186$
64.1-a4 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23287.10750$ 1.52868 \( \frac{1331}{8} \) \( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( 11 a^{5} + a^{4} - 51 a^{3} - 5 a^{2} + 55 a + 15\) , \( 49 a^{5} - 8 a^{4} - 244 a^{3} + 3 a^{2} + 281 a + 64\bigr] \) ${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{5}-5a^{3}+5a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+6a-1\right){x}^{2}+\left(11a^{5}+a^{4}-51a^{3}-5a^{2}+55a+15\right){x}+49a^{5}-8a^{4}-244a^{3}+3a^{2}+281a+64$
64.1-a5 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $23287.10750$ 1.52868 \( \frac{461373}{2} a^{4} - \frac{461373}{2} a^{3} - 922746 a^{2} + 461373 a + \frac{321323}{2} \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a\) , \( -2 a^{4} + 7 a^{2} - 3\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+{x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+4a\right){x}-2a^{4}+7a^{2}-3$
64.1-a6 64.1-a \(\Q(\zeta_{13})^+\) \( 2^{6} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.490374880$ 1.52868 \( \frac{1250637664527933}{32} a^{4} - \frac{1250637664527933}{32} a^{3} - \frac{1250637664527933}{8} a^{2} + \frac{1250637664527933}{16} a + \frac{871975048120043}{32} \) \( \bigl[1\) , \( 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( 28 a^{4} - 29 a^{3} - 112 a^{2} + 58 a + 58\) , \( 51 a^{4} - 52 a^{3} - 205 a^{2} + 104 a - 3\bigr] \) ${y}^2+{x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){y}={x}^{3}+{x}^{2}+\left(28a^{4}-29a^{3}-112a^{2}+58a+58\right){x}+51a^{4}-52a^{3}-205a^{2}+104a-3$
64.1-b1 64.1-b \(\Q(\zeta_{13})^+\) \( 2^{6} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.188700458$ $0.313224695$ 2.51505 \( -\frac{38575685889}{16384} \) \( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( 1801 a^{5} + 962 a^{4} - 7561 a^{3} - 4471 a^{2} + 4023 a + 1051\) , \( 70970 a^{5} + 36003 a^{4} - 301077 a^{3} - 170680 a^{2} + 170108 a + 46396\bigr] \) ${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}^{2}+\left(1801a^{5}+962a^{4}-7561a^{3}-4471a^{2}+4023a+1051\right){x}+70970a^{5}+36003a^{4}-301077a^{3}-170680a^{2}+170108a+46396$
64.1-b2 64.1-b \(\Q(\zeta_{13})^+\) \( 2^{6} \) $1$ $\Z/7\Z$ $\mathrm{SU}(2)$ $0.169814351$ $36850.57220$ 2.51505 \( \frac{351}{4} \) \( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{5} + 2 a^{4} - a^{3} - a^{2} + 3 a + 1\) , \( -20 a^{5} - 7 a^{4} + 93 a^{3} + 50 a^{2} - 52 a - 14\bigr] \) ${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}^{2}+\left(a^{5}+2a^{4}-a^{3}-a^{2}+3a+1\right){x}-20a^{5}-7a^{4}+93a^{3}+50a^{2}-52a-14$
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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.