Elliptic curves over Q(ζ13)+\Q(\zeta_{13})^+ of conductor 64.1

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
64.1-a1	64.1-a	$6$	$45$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{30}$	$77.00376$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3, 5$	3B, 5B.1.2	$625$	$1$	$1$	$1.490374880$	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	$6$	$45$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{6}$	$77.00376$	$(2)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3, 5$	3B, 5B.1.1	$1$	$1$	$1$	$23287.10750$	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	$6$	$45$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{90}$	$77.00376$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3, 5$	3Cs, 5B.1.2	$625$	$1$	$1$	$1.490374880$	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	$6$	$45$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{18}$	$77.00376$	$(2)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3, 5$	3Cs, 5B.1.1	$1$	$1$	$1$	$23287.10750$	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	$6$	$45$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{6}$	$77.00376$	$(2)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3, 5$	3B, 5B.1.1	$1$	$1$	$1$	$23287.10750$	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	$6$	$45$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{30}$	$77.00376$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3, 5$	3B, 5B.1.2	$625$	$1$	$1$	$1.490374880$	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	$2$	$7$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{84}$	$77.00376$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$7$	7B.1.3	$49$	$2 \cdot 7$	$1.188700458$	$0.313224695$	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	$2$	$7$	$\Q(\zeta_{13})^+$	$6$	$[6, 0]$	64.1	$2^{6}$	$2^{12}$	$77.00376$	$(2)$	$1$	$\Z/7\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$7$	7B.1.1	$1$	$2$	$0.169814351$	$36850.57220$	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.