Elliptic curves over Q\Q of conductor 75

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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
75.a1	75c2	75.a	75c	$2$	$5$	$3 \cdot 5^{2}$	$- 3 \cdot 5^{10}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.24.0.3	5B.1.2	$30$	$48$	$1$	$1$	$1$		$0$	$30$	$0.211621$	$-102400/3$	$1.04391$	$6.41123$	$[0, 1, 1, -208, -1256]$	$y^2+y=x^3+x^2-208x-1256$	5.24.0-5.a.2.2, 6.2.0.a.1, 30.48.1-30.d.2.4	$[]$
75.a2	75c1	75.a	75c	$2$	$5$	$3 \cdot 5^{2}$	$- 3^{5} \cdot 5^{2}$	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$			$5$	5.24.0.1	5B.1.1	$30$	$48$	$1$	$1$	$1$		$4$	$6$	$-0.593099$	$20480/243$	$1.13104$	$3.73288$	$[0, 1, 1, 2, 4]$	$y^2+y=x^3+x^2+2x+4$	5.24.0-5.a.1.2, 6.2.0.a.1, 30.48.1-30.d.1.4	$[]$
75.b1	75b7	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$3^{4} \cdot 5^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.168	2B	$480$	$768$	$13$	$1$	$1$		$0$	$96$	$1.095589$	$1114544804970241/405$	$1.07354$	$10.26149$	$[1, 0, 1, -54001, -4834477]$	$y^2+xy+y=x^3-54001x-4834477$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.6, 10.6.0.a.1, 16.96.0-16.x.2.5, $\ldots$	$[]$
75.b2	75b5	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$3^{8} \cdot 5^{8}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.31	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$48$	$0.749015$	$272223782641/164025$	$1.03897$	$8.33506$	$[1, 0, 1, -3376, -75727]$	$y^2+xy+y=x^3-3376x-75727$	2.6.0.a.1, 4.24.0-4.b.1.2, 8.96.0-8.k.1.7, 20.48.0-20.c.1.3, 40.192.1-40.cc.2.5, $\ldots$	$[]$
75.b3	75b8	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$- 3^{16} \cdot 5^{7}$	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.121	2B	$480$	$768$	$13$	$1$	$1$		$2$	$96$	$1.095589$	$-147281603041/215233605$	$1.05949$	$8.48461$	$[1, 0, 1, -2751, -104477]$	$y^2+xy+y=x^3-2751x-104477$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.2.7, 16.96.0-16.u.2.5, 20.24.0-20.h.1.2, $\ldots$	$[]$
75.b4	75b4	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$3 \cdot 5^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.29	2B	$480$	$768$	$13$	$1$	$1$		$0$	$24$	$0.402442$	$56667352321/15$	$1.03019$	$7.97155$	$[1, 0, 1, -2001, 34273]$	$y^2+xy+y=x^3-2001x+34273$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.1, 16.48.0-16.g.1.1, $\ldots$	$[]$
75.b5	75b3	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$3^{4} \cdot 5^{10}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.77	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$24$	$0.402442$	$111284641/50625$	$1.02534$	$6.52792$	$[1, 0, 1, -251, -727]$	$y^2+xy+y=x^3-251x-727$	2.6.0.a.1, 4.24.0.b.1, 8.96.0-8.b.2.3, 20.48.0-4.b.1.1, 24.192.1-24.n.1.9, $\ldots$	$[]$
75.b6	75b2	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$3^{2} \cdot 5^{8}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.35	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$12$	$0.055868$	$13997521/225$	$0.96230$	$6.04773$	$[1, 0, 1, -126, 523]$	$y^2+xy+y=x^3-126x+523$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.3, 12.24.0-4.b.1.2, 16.96.0-16.d.2.8, $\ldots$	$[]$
75.b7	75b1	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$- 3 \cdot 5^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.29	2B	$480$	$768$	$13$	$1$	$1$		$1$	$6$	$-0.290706$	$-1/15$	$1.19808$	$4.59050$	$[1, 0, 1, -1, 23]$	$y^2+xy+y=x^3-x+23$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.2, 16.48.0-16.g.1.1, $\ldots$	$[]$
75.b8	75b6	75.b	75b	$8$	$16$	$3 \cdot 5^{2}$	$- 3^{2} \cdot 5^{14}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.197	2B	$480$	$768$	$13$	$1$	$1$		$0$	$48$	$0.749015$	$4733169839/3515625$	$1.05585$	$7.39654$	$[1, 0, 1, 874, -5227]$	$y^2+xy+y=x^3+874x-5227$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 16.96.0-8.n.2.2, 20.24.0-4.d.1.1, $\ldots$	$[]$
75.c1	75a1	75.c	75a	$2$	$5$	$3 \cdot 5^{2}$	$- 3 \cdot 5^{4}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.24.0.4	5B.1.3	$30$	$48$	$1$	$1$	$1$		$0$	$6$	$-0.593099$	$-102400/3$	$1.04391$	$4.17460$	$[0, -1, 1, -8, -7]$	$y^2+y=x^3-x^2-8x-7$	5.24.0-5.a.2.1, 6.2.0.a.1, 30.48.1-30.d.2.3	$[]$
75.c2	75a2	75.c	75a	$2$	$5$	$3 \cdot 5^{2}$	$- 3^{5} \cdot 5^{8}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.24.0.2	5B.1.4	$30$	$48$	$1$	$1$	$1$		$0$	$30$	$0.211621$	$20480/243$	$1.13104$	$5.96951$	$[0, -1, 1, 42, 443]$	$y^2+y=x^3-x^2+42x+443$	5.24.0-5.a.1.1, 6.2.0.a.1, 30.48.1-30.d.1.3	$[]$

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