Elliptic curves over Q(−13)\Q(\sqrt{-13})

Results (1-50 of 664 matches)

  Download displayed columns for results to

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
16.1-a1	16.1-a	$2$	$5$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{42}$	$1.28875$	$(2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3, 5$	3Ns, 5B	$1$	$2$	$1.688026059$	$0.987129325$	1.848593902	$-\frac{1680914269}{32768}$	$\bigl[a + 1$ , $-a$ , $0$ , $a + 101$ , $-124 a - 99\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(a+101\right){x}-124a-99$
16.1-a2	16.1-a	$2$	$5$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{18}$	$1.28875$	$(2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3, 5$	3Ns, 5B	$1$	$2$	$0.337605211$	$4.935646628$	1.848593902	$\frac{1331}{8}$	$\bigl[a + 1$ , $-a$ , $0$ , $a + 1$ , $1\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(a+1\right){x}+1$
16.1-b1	16.1-b	$2$	$5$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{42}$	$1.28875$	$(2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3, 5$	3Ns, 5B	$1$	$2$	$1.688026059$	$0.987129325$	1.848593902	$-\frac{1680914269}{32768}$	$\bigl[a + 1$ , $0$ , $0$ , $-a + 101$ , $124 a - 99\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+101\right){x}+124a-99$
16.1-b2	16.1-b	$2$	$5$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{18}$	$1.28875$	$(2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$3, 5$	3Ns, 5B	$1$	$2$	$0.337605211$	$4.935646628$	1.848593902	$\frac{1331}{8}$	$\bigl[a + 1$ , $0$ , $0$ , $-a + 1$ , $1\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}+1$
26.1-a1	26.1-a	$3$	$9$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{18} \cdot 13^{2}$	$1.45507$	$(2,a+1), (a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	$2^{2}$	$1$	$0.896934130$	0.995059076	$-\frac{10730978619193}{6656}$	$\bigl[1$ , $0$ , $1$ , $-460$ , $-3830\bigr]$	${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$
26.1-a2	26.1-a	$3$	$9$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{6} \cdot 13^{6}$	$1.45507$	$(2,a+1), (a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	$2^{2} \cdot 3$	$1$	$2.690802392$	0.995059076	$-\frac{10218313}{17576}$	$\bigl[1$ , $0$ , $1$ , $-5$ , $-8\bigr]$	${y}^2+{x}{y}+{y}={x}^3-5{x}-8$
26.1-a3	26.1-a	$3$	$9$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{2} \cdot 13^{2}$	$1.45507$	$(2,a+1), (a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	$2^{2}$	$1$	$8.072407178$	0.995059076	$\frac{12167}{26}$	$\bigl[1$ , $0$ , $1$ , $0$ , $0\bigr]$	${y}^2+{x}{y}+{y}={x}^3$
26.1-b1	26.1-b	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{2} \cdot 13^{14}$	$1.45507$	$(2,a+1), (a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$7$	7B.6.1	$1$	$2^{2}$	$1.383448027$	$0.560128502$	1.719367970	$-\frac{1064019559329}{125497034}$	$\bigl[a$ , $1$ , $0$ , $-211$ , $1469\bigr]$	${y}^2+a{x}{y}={x}^3+{x}^2-211{x}+1469$
26.1-b2	26.1-b	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{14} \cdot 13^{2}$	$1.45507$	$(2,a+1), (a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$7$	7B.6.1	$1$	$2^{2}$	$0.197635432$	$3.920899519$	1.719367970	$-\frac{2146689}{1664}$	$\bigl[a$ , $1$ , $0$ , $-1$ , $-1\bigr]$	${y}^2+a{x}{y}={x}^3+{x}^2-{x}-1$
26.1-c1	26.1-c	$3$	$9$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{18} \cdot 13^{2}$	$1.45507$	$(2,a+1), (a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	$2^{2} \cdot 3^{2}$	$0.166288191$	$0.896934130$	2.978398339	$-\frac{10730978619193}{6656}$	$\bigl[a$ , $0$ , $0$ , $-456$ , $4288\bigr]$	${y}^2+a{x}{y}={x}^3-456{x}+4288$
26.1-c2	26.1-c	$3$	$9$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{6} \cdot 13^{6}$	$1.45507$	$(2,a+1), (a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	$2^{2} \cdot 3^{2}$	$0.055429397$	$2.690802392$	2.978398339	$-\frac{10218313}{17576}$	$\bigl[a$ , $0$ , $0$ , $-1$ , $11\bigr]$	${y}^2+a{x}{y}={x}^3-{x}+11$
26.1-c3	26.1-c	$3$	$9$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{2} \cdot 13^{2}$	$1.45507$	$(2,a+1), (a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs	$1$	$2^{2}$	$0.166288191$	$8.072407178$	2.978398339	$\frac{12167}{26}$	$\bigl[a$ , $0$ , $0$ , $4$ , $-2\bigr]$	${y}^2+a{x}{y}={x}^3+4{x}-2$
26.1-d1	26.1-d	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{2} \cdot 13^{14}$	$1.45507$	$(2,a+1), (a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$7$	7B.1.1	$4$	$2^{2}$	$1$	$0.560128502$	2.485627123	$-\frac{1064019559329}{125497034}$	$\bigl[1$ , $-1$ , $1$ , $-213$ , $-1257\bigr]$	${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$
26.1-d2	26.1-d	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	26.1	$2 \cdot 13$	$2^{14} \cdot 13^{2}$	$1.45507$	$(2,a+1), (a)$	0	$\Z/7\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$7$	7B.1.1	$4$	$2^{2} \cdot 7$	$1$	$3.920899519$	2.485627123	$-\frac{2146689}{1664}$	$\bigl[1$ , $-1$ , $1$ , $-3$ , $3\bigr]$	${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$
49.1-a1	49.1-a	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.1	$7^{2}$	$7^{6}$	$1.70486$	$(7,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B	$1$	$1$	$1$	$4.561503326$	1.265133395	$-3703 a + 11250$	$\bigl[a$ , $a + 1$ , $a + 1$ , $-a + 5$ , $-a - 2\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-a+5\right){x}-a-2$
49.1-a2	49.1-a	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.1	$7^{2}$	$2^{12} \cdot 7^{6}$	$1.70486$	$(7,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B	$1$	$1$	$1$	$4.561503326$	1.265133395	$3703 a + 11250$	$\bigl[a + 1$ , $a + 1$ , $a + 1$ , $-6 a - 13$ , $a + 43\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-6a-13\right){x}+a+43$
49.1-b1	49.1-b	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.1	$7^{2}$	$7^{6}$	$1.70486$	$(7,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B.2.3	$1$	$1$	$1$	$4.561503326$	1.265133395	$-3703 a + 11250$	$\bigl[1$ , $-a - 1$ , $a$ , $a - 3$ , $11\bigr]$	${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(a-3\right){x}+11$
49.1-b2	49.1-b	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.1	$7^{2}$	$2^{12} \cdot 7^{6}$	$1.70486$	$(7,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B.2.3	$1$	$1$	$1$	$4.561503326$	1.265133395	$3703 a + 11250$	$\bigl[a + 1$ , $a - 1$ , $0$ , $-7 a - 15$ , $-6 a + 37\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-7a-15\right){x}-6a+37$
49.3-a1	49.3-a	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.3	$7^{2}$	$2^{12} \cdot 7^{6}$	$1.70486$	$(7,a+6)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B	$1$	$1$	$1$	$4.561503326$	1.265133395	$-3703 a + 11250$	$\bigl[a + 1$ , $a + 1$ , $0$ , $a - 19$ , $-14 a + 1\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(a-19\right){x}-14a+1$
49.3-a2	49.3-a	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.3	$7^{2}$	$7^{6}$	$1.70486$	$(7,a+6)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B	$1$	$1$	$1$	$4.561503326$	1.265133395	$3703 a + 11250$	$\bigl[a$ , $-a + 1$ , $a + 1$ , $5$ , $-2\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+5{x}-2$
49.3-b1	49.3-b	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.3	$7^{2}$	$2^{12} \cdot 7^{6}$	$1.70486$	$(7,a+6)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B.2.1	$1$	$1$	$1$	$4.561503326$	1.265133395	$-3703 a + 11250$	$\bigl[a + 1$ , $a - 1$ , $a + 1$ , $-2 a - 9$ , $-3 a + 1\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-2a-9\right){x}-3a+1$
49.3-b2	49.3-b	$2$	$7$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	49.3	$7^{2}$	$7^{6}$	$1.70486$	$(7,a+6)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 7$	3Nn, 7B.2.1	$1$	$1$	$1$	$4.561503326$	1.265133395	$3703 a + 11250$	$\bigl[1$ , $a - 1$ , $a$ , $-2 a - 3$ , $11\bigr]$	${y}^2+{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-2a-3\right){x}+11$
52.1-a1	52.1-a	$2$	$2$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	52.1	$2^{2} \cdot 13$	$2^{16} \cdot 13^{4}$	$1.73038$	$(2,a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1$	$4.738620278$	0.657128399	$\frac{432}{169}$	$\bigl[0$ , $0$ , $0$ , $1$ , $-10\bigr]$	${y}^2={x}^3+{x}-10$
52.1-a2	52.1-a	$2$	$2$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	52.1	$2^{2} \cdot 13$	$2^{8} \cdot 13^{2}$	$1.73038$	$(2,a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1$	$4.738620278$	0.657128399	$\frac{442368}{13}$	$\bigl[0$ , $0$ , $0$ , $-4$ , $-3\bigr]$	${y}^2={x}^3-4{x}-3$
52.1-b1	52.1-b	$2$	$2$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	52.1	$2^{2} \cdot 13$	$2^{16} \cdot 13^{4}$	$1.73038$	$(2,a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2 \cdot 3$	$1$	$4.738620278$	1.971385198	$\frac{432}{169}$	$\bigl[0$ , $0$ , $0$ , $1$ , $10\bigr]$	${y}^2={x}^3+{x}+10$
52.1-b2	52.1-b	$2$	$2$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	52.1	$2^{2} \cdot 13$	$2^{8} \cdot 13^{2}$	$1.73038$	$(2,a+1), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2 \cdot 3$	$1$	$4.738620278$	1.971385198	$\frac{442368}{13}$	$\bigl[0$ , $0$ , $0$ , $-4$ , $3\bigr]$	${y}^2={x}^3-4{x}+3$
64.1-a1	64.1-a	$1$	$1$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{6}$	$1.82257$	$(2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3Cn	$1$	$1$	$1$	$7.681576726$	2.130486058	$-74088$	$\bigl[a + 1$ , $a$ , $a + 1$ , $-4 a + 1$ , $10\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+1\right){x}+10$
64.1-b1	64.1-b	$4$	$4$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{12}$	$1.82257$	$(2,a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	$2$	$5.832511736$	$6.875185818$	2.780407135	$1728$	$\bigl[0$ , $0$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^3-{x}$
64.1-b2	64.1-b	$4$	$4$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{24}$	$1.82257$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	$2^{2}$	$2.916255868$	$6.875185818$	2.780407135	$1728$	$\bigl[0$ , $0$ , $0$ , $4$ , $0\bigr]$	${y}^2={x}^3+4{x}$
64.1-b3	64.1-b	$4$	$4$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{18}$	$1.82257$	$(2,a+1)$	$1$	$\Z/2\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	$1$	$2.916255868$	$6.875185818$	2.780407135	$287496$	$\bigl[0$ , $0$ , $0$ , $-11$ , $-14\bigr]$	${y}^2={x}^3-11{x}-14$
64.1-b4	64.1-b	$4$	$4$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{18}$	$1.82257$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	$1$	$11.66502347$	$6.875185818$	2.780407135	$287496$	$\bigl[0$ , $0$ , $0$ , $-11$ , $14\bigr]$	${y}^2={x}^3-11{x}+14$
64.1-c1	64.1-c	$1$	$1$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{6}$	$1.82257$	$(2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3Cn	$1$	$1$	$1$	$7.681576726$	2.130486058	$-74088$	$\bigl[a + 1$ , $a$ , $0$ , $-3 a - 5$ , $a + 7\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-3a-5\right){x}+a+7$
72.1-a1	72.1-a	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{22} \cdot 3^{16}$	$1.87704$	$(2,a+1), (3)$	$1$	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$11.45024622$	$1.817673508$	2.886217342	$\frac{207646}{6561}$	$\bigl[0$ , $1$ , $0$ , $16$ , $180\bigr]$	${y}^2={x}^3+{x}^2+16{x}+180$
72.1-a2	72.1-a	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{8} \cdot 3^{2}$	$1.87704$	$(2,a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2$	$1.431280778$	$7.270694035$	2.886217342	$\frac{2048}{3}$	$\bigl[0$ , $1$ , $0$ , $1$ , $0\bigr]$	${y}^2={x}^3+{x}^2+{x}$
72.1-a3	72.1-a	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{16} \cdot 3^{4}$	$1.87704$	$(2,a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{2}$	$2.862561557$	$7.270694035$	2.886217342	$\frac{35152}{9}$	$\bigl[0$ , $1$ , $0$ , $-4$ , $-4\bigr]$	${y}^2={x}^3+{x}^2-4{x}-4$
72.1-a4	72.1-a	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{20} \cdot 3^{8}$	$1.87704$	$(2,a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$5.725123114$	$3.635347017$	2.886217342	$\frac{1556068}{81}$	$\bigl[0$ , $1$ , $0$ , $-24$ , $36\bigr]$	${y}^2={x}^3+{x}^2-24{x}+36$
72.1-a5	72.1-a	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{20} \cdot 3^{2}$	$1.87704$	$(2,a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{2}$	$1.431280778$	$3.635347017$	2.886217342	$\frac{28756228}{3}$	$\bigl[0$ , $1$ , $0$ , $-64$ , $-220\bigr]$	${y}^2={x}^3+{x}^2-64{x}-220$
72.1-a6	72.1-a	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{22} \cdot 3^{4}$	$1.87704$	$(2,a+1), (3)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{2}$	$11.45024622$	$1.817673508$	2.886217342	$\frac{3065617154}{9}$	$\bigl[0$ , $1$ , $0$ , $-384$ , $2772\bigr]$	${y}^2={x}^3+{x}^2-384{x}+2772$
72.1-b1	72.1-b	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{22} \cdot 3^{16}$	$1.87704$	$(2,a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1$	$1.817673508$	2.016527704	$\frac{207646}{6561}$	$\bigl[0$ , $-1$ , $0$ , $16$ , $-180\bigr]$	${y}^2={x}^3-{x}^2+16{x}-180$
72.1-b2	72.1-b	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{8} \cdot 3^{2}$	$1.87704$	$(2,a+1), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	$2^{2}$	$1$	$7.270694035$	2.016527704	$\frac{2048}{3}$	$\bigl[0$ , $-1$ , $0$ , $1$ , $0\bigr]$	${y}^2={x}^3-{x}^2+{x}$
72.1-b3	72.1-b	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{16} \cdot 3^{4}$	$1.87704$	$(2,a+1), (3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$16$	$2^{2}$	$1$	$7.270694035$	2.016527704	$\frac{35152}{9}$	$\bigl[0$ , $-1$ , $0$ , $-4$ , $4\bigr]$	${y}^2={x}^3-{x}^2-4{x}+4$
72.1-b4	72.1-b	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{20} \cdot 3^{8}$	$1.87704$	$(2,a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	$2^{3}$	$1$	$3.635347017$	2.016527704	$\frac{1556068}{81}$	$\bigl[0$ , $-1$ , $0$ , $-24$ , $-36\bigr]$	${y}^2={x}^3-{x}^2-24{x}-36$
72.1-b5	72.1-b	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{20} \cdot 3^{2}$	$1.87704$	$(2,a+1), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$16$	$2$	$1$	$3.635347017$	2.016527704	$\frac{28756228}{3}$	$\bigl[0$ , $-1$ , $0$ , $-64$ , $220\bigr]$	${y}^2={x}^3-{x}^2-64{x}+220$
72.1-b6	72.1-b	$6$	$8$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	72.1	$2^{3} \cdot 3^{2}$	$2^{22} \cdot 3^{4}$	$1.87704$	$(2,a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	$2^{2}$	$1$	$1.817673508$	2.016527704	$\frac{3065617154}{9}$	$\bigl[0$ , $-1$ , $0$ , $-384$ , $-2772\bigr]$	${y}^2={x}^3-{x}^2-384{x}-2772$
98.2-a1	98.2-a	$6$	$18$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	98.2	$2 \cdot 7^{2}$	$2^{36} \cdot 7^{2}$	$2.02743$	$(2,a+1), (7,a+1), (7,a+6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2$	$10.40550172$	$0.875417135$	2.526424896	$-\frac{548347731625}{1835008}$	$\bigl[1$ , $0$ , $1$ , $-171$ , $-874\bigr]$	${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
98.2-a2	98.2-a	$6$	$18$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	98.2	$2 \cdot 7^{2}$	$2^{4} \cdot 7^{2}$	$2.02743$	$(2,a+1), (7,a+1), (7,a+6)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2$	$10.40550172$	$7.878754216$	2.526424896	$-\frac{15625}{28}$	$\bigl[1$ , $0$ , $1$ , $-1$ , $0\bigr]$	${y}^2+{x}{y}+{y}={x}^3-{x}$
98.2-a3	98.2-a	$6$	$18$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	98.2	$2 \cdot 7^{2}$	$2^{12} \cdot 7^{6}$	$2.02743$	$(2,a+1), (7,a+1), (7,a+6)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2 \cdot 3^{2}$	$3.468500574$	$2.626251405$	2.526424896	$\frac{9938375}{21952}$	$\bigl[1$ , $0$ , $1$ , $4$ , $-6\bigr]$	${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
98.2-a4	98.2-a	$6$	$18$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	98.2	$2 \cdot 7^{2}$	$2^{6} \cdot 7^{12}$	$2.02743$	$(2,a+1), (7,a+1), (7,a+6)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{3} \cdot 3^{2}$	$1.734250287$	$1.313125702$	2.526424896	$\frac{4956477625}{941192}$	$\bigl[1$ , $0$ , $1$ , $-36$ , $-70\bigr]$	${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
98.2-a5	98.2-a	$6$	$18$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	98.2	$2 \cdot 7^{2}$	$2^{2} \cdot 7^{4}$	$2.02743$	$(2,a+1), (7,a+1), (7,a+6)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{3}$	$5.202750861$	$3.939377108$	2.526424896	$\frac{128787625}{98}$	$\bigl[1$ , $0$ , $1$ , $-11$ , $12\bigr]$	${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
98.2-a6	98.2-a	$6$	$18$	$\Q(\sqrt{-13})$	$2$	$[0, 1]$	98.2	$2 \cdot 7^{2}$	$2^{18} \cdot 7^{4}$	$2.02743$	$(2,a+1), (7,a+1), (7,a+6)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{3}$	$5.202750861$	$0.437708567$	2.526424896	$\frac{2251439055699625}{25088}$	$\bigl[1$ , $0$ , $1$ , $-2731$ , $-55146\bigr]$	${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$

  Download displayed columns for results to

  *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.