Elliptic curves over $\Q$ of conductor 15

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
15.a1	15a5	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( 3^{4} \cdot 5 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.148	2B	$480$	$768$	$13$	$1$	$1$		$0$	$4$	$0.290870$	$1114544804970241/405$	$1.07354$	$12.79416$	$[1, 1, 1, -2160, -39540]$	\(y^2+xy+y=x^3+x^2-2160x-39540\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 10.6.0.a.1, 16.96.0-16.x.2.4, $\ldots$	$[]$
15.a2	15a2	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.58	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$2$	$-0.055704$	$272223782641/164025$	$1.03897$	$9.72282$	$[1, 1, 1, -135, -660]$	\(y^2+xy+y=x^3+x^2-135x-660\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.k.1.1, 20.48.0-20.c.1.2, 40.192.1-40.cc.2.4, $\ldots$	$[]$
15.a3	15a6	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( - 3^{16} \cdot 5 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.153	2B	$480$	$768$	$13$	$1$	$1$		$0$	$4$	$0.290870$	$-147281603041/215233605$	$1.05949$	$9.96125$	$[1, 1, 1, -110, -880]$	\(y^2+xy+y=x^3+x^2-110x-880\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 16.96.0-16.u.2.3, 20.24.0-20.h.1.1, $\ldots$	$[]$
15.a4	15a7	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( 3 \cdot 5 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.5	2B	$480$	$768$	$13$	$1$	$1$		$2$	$4$	$-0.402277$	$56667352321/15$	$1.03019$	$9.14328$	$[1, 1, 1, -80, 242]$	\(y^2+xy+y=x^3+x^2-80x+242\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 24.48.0-24.by.2.3, $\ldots$	$[]$
15.a5	15a1	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( 3^{4} \cdot 5^{4} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.3	2Cs	$240$	$768$	$13$	$1$	$1$		$6$	$1$	$-0.402277$	$111284641/50625$	$1.02534$	$6.84168$	$[1, 1, 1, -10, -10]$	\(y^2+xy+y=x^3+x^2-10x-10\)	2.6.0.a.1, 4.48.0-4.b.1.1, 8.96.0-8.b.2.9, 24.192.1-24.n.1.1, 40.192.1-40.s.1.5, $\ldots$	$[]$
15.a6	15a3	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.7	2Cs	$240$	$768$	$13$	$1$	$1$		$6$	$2$	$-0.748851$	$13997521/225$	$0.96230$	$6.07610$	$[1, 1, 1, -5, 2]$	\(y^2+xy+y=x^3+x^2-5x+2\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.i.1.10, 16.96.0-16.d.2.3, 24.96.0-24.bb.2.5, $\ldots$	$[]$
15.a7	15a8	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( - 3 \cdot 5 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.5	2B	$480$	$768$	$13$	$1$	$1$		$3$	$4$	$-1.095425$	$-1/15$	$1.19808$	$3.75281$	$[1, 1, 1, 0, 0]$	\(y^2+xy+y=x^3+x^2\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.g.1.2, 24.48.0-24.bz.1.3, $\ldots$	$[]$
15.a8	15a4	15.a	15a	$8$	$16$	\( 3 \cdot 5 \)	\( - 3^{2} \cdot 5^{8} \)	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.99	2B	$480$	$768$	$13$	$1$	$1$		$6$	$2$	$-0.055704$	$4733169839/3515625$	$1.05585$	$8.22653$	$[1, 1, 1, 35, -28]$	\(y^2+xy+y=x^3+x^2+35x-28\)	2.3.0.a.1, 4.24.0-4.d.1.1, 8.96.0-8.n.2.5, 24.192.1-24.cv.2.2, 80.192.1.?, $\ldots$	$[]$

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