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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images
11.a1 11.a \( 11 \) $0$ $\mathsf{trivial}$ $1$ $[0, -1, 1, -7820, -263580]$ \(y^2+y=x^3-x^2-7820x-263580\) 5.24.0-5.a.2.2, 22.2.0.a.1, 25.120.0-25.a.2.2, 110.48.1.?, 275.600.12.?, $\ldots$
11.a2 11.a \( 11 \) $0$ $\Z/5\Z$ $1$ $[0, -1, 1, -10, -20]$ \(y^2+y=x^3-x^2-10x-20\) 5.120.0-5.a.1.2, 22.2.0.a.1, 110.240.5.?, 275.600.12.?, 550.1200.37.?
11.a3 11.a \( 11 \) $0$ $\Z/5\Z$ $1$ $[0, -1, 1, 0, 0]$ \(y^2+y=x^3-x^2\) 5.24.0-5.a.1.2, 22.2.0.a.1, 25.120.0-25.a.1.2, 110.48.1.?, 275.600.12.?, $\ldots$
14.a1 14.a \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -2731, -55146]$ \(y^2+xy+y=x^3-2731x-55146\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.b.1, 9.24.0-9.a.1.1, $\ldots$
14.a2 14.a \( 2 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -171, -874]$ \(y^2+xy+y=x^3-171x-874\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.c.1, 9.24.0-9.a.1.1, $\ldots$
14.a3 14.a \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $[1, 0, 1, -36, -70]$ \(y^2+xy+y=x^3-36x-70\) 2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 8.6.0.b.1, 24.144.1-24.h.1.1, $\ldots$
14.a4 14.a \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $[1, 0, 1, -11, 12]$ \(y^2+xy+y=x^3-11x+12\) 2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.b.1, 9.24.0-9.a.1.2, $\ldots$
14.a5 14.a \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $[1, 0, 1, -1, 0]$ \(y^2+xy+y=x^3-x\) 2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.c.1, 9.24.0-9.a.1.2, $\ldots$
14.a6 14.a \( 2 \cdot 7 \) $0$ $\Z/6\Z$ $1$ $[1, 0, 1, 4, -6]$ \(y^2+xy+y=x^3+4x-6\) 2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$
15.a1 15.a \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -2160, -39540]$ \(y^2+xy+y=x^3+x^2-2160x-39540\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 1, -135, -660]$ \(y^2+xy+y=x^3+x^2-135x-660\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -110, -880]$ \(y^2+xy+y=x^3+x^2-110x-880\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 1, -80, 242]$ \(y^2+xy+y=x^3+x^2-80x+242\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $[1, 1, 1, -10, -10]$ \(y^2+xy+y=x^3+x^2-10x-10\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $[1, 1, 1, -5, 2]$ \(y^2+xy+y=x^3+x^2-5x+2\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 1, 0, 0]$ \(y^2+xy+y=x^3+x^2\) 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 15.a \( 3 \cdot 5 \) $0$ $\Z/8\Z$ $1$ $[1, 1, 1, 35, -28]$ \(y^2+xy+y=x^3+x^2+35x-28\) 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.?, $\ldots$
17.a1 17.a \( 17 \) $0$ $\Z/2\Z$ $1$ $[1, -1, 1, -91, -310]$ \(y^2+xy+y=x^3-x^2-91x-310\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 16.48.0-16.j.1.3, 32.96.0-32.f.2.1, $\ldots$
17.a2 17.a \( 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 1, -6, -4]$ \(y^2+xy+y=x^3-x^2-6x-4\) 2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.f.1.1, 16.96.0-16.c.2.2, 68.48.0-68.b.1.1, $\ldots$
17.a3 17.a \( 17 \) $0$ $\Z/4\Z$ $1$ $[1, -1, 1, -1, -14]$ \(y^2+xy+y=x^3-x^2-x-14\) 2.3.0.a.1, 4.24.0-4.d.1.1, 8.48.0-8.t.1.2, 16.96.0-16.m.2.1, 136.96.1.?, $\ldots$
17.a4 17.a \( 17 \) $0$ $\Z/4\Z$ $1$ $[1, -1, 1, -1, 0]$ \(y^2+xy+y=x^3-x^2-x\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 16.48.0-16.j.1.1, 32.96.0-32.f.2.2, $\ldots$
19.a1 19.a \( 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, 1, 1, -769, -8470]$ \(y^2+y=x^3+x^2-769x-8470\) 3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 27.72.0-27.a.1.1, 38.2.0.a.1, 114.16.0.?, $\ldots$
19.a2 19.a \( 19 \) $0$ $\Z/3\Z$ $1$ $[0, 1, 1, -9, -15]$ \(y^2+y=x^3+x^2-9x-15\) 3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$
19.a3 19.a \( 19 \) $0$ $\Z/3\Z$ $1$ $[0, 1, 1, 1, 0]$ \(y^2+y=x^3+x^2+x\) 3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$
20.a1 20.a \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $[0, 1, 0, -41, -116]$ \(y^2=x^3+x^2-41x-116\) 2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.b.1, 6.24.0-6.a.1.2, 8.12.0-4.b.1.2, $\ldots$
20.a2 20.a \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $[0, 1, 0, -36, -140]$ \(y^2=x^3+x^2-36x-140\) 2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.a.1, 6.24.0-6.a.1.2, 8.12.0-4.a.1.1, $\ldots$
20.a3 20.a \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $[0, 1, 0, -1, 0]$ \(y^2=x^3+x^2-x\) 2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.b.1, 6.24.0-6.a.1.4, 8.12.0-4.b.1.2, $\ldots$
20.a4 20.a \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $[0, 1, 0, 4, 4]$ \(y^2=x^3+x^2+4x+4\) 2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.a.1, 6.24.0-6.a.1.4, 8.12.0-4.a.1.1, $\ldots$
21.a1 21.a \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -784, -8515]$ \(y^2+xy=x^3-784x-8515\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 12.24.0-12.h.1.1, 16.48.0-16.e.2.5, $\ldots$
21.a2 21.a \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 0, -49, -136]$ \(y^2+xy=x^3-49x-136\) 2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 12.48.0-12.c.1.3, 24.96.0-24.j.2.5, $\ldots$
21.a3 21.a \( 3 \cdot 7 \) $0$ $\Z/8\Z$ $1$ $[1, 0, 0, -39, 90]$ \(y^2+xy=x^3-39x+90\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 28.24.0-28.h.1.2, 48.96.0-48.bf.1.3, $\ldots$
21.a4 21.a \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -34, -217]$ \(y^2+xy=x^3-34x-217\) 2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.bb.2.3, 12.24.0-12.g.1.1, $\ldots$
21.a5 21.a \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $[1, 0, 0, -4, -1]$ \(y^2+xy=x^3-4x-1\) 2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 24.96.0-24.w.2.6, 28.48.0-28.c.1.1, $\ldots$
21.a6 21.a \( 3 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 0, 1, 0]$ \(y^2+xy=x^3+x\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 14.6.0.b.1, 16.48.0-16.e.1.2, $\ldots$
24.a1 24.a \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $[0, -1, 0, -384, -2772]$ \(y^2=x^3-x^2-384x-2772\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 16.96.0-16.l.1.6, 24.96.0-24.bf.1.4, $\ldots$
24.a2 24.a \( 2^{3} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $[0, -1, 0, -64, 220]$ \(y^2=x^3-x^2-64x+220\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 12.24.0-12.h.1.2, 16.96.0-16.bb.2.4, $\ldots$
24.a3 24.a \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[0, -1, 0, -24, -36]$ \(y^2=x^3-x^2-24x-36\) 2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.e.2.2, 24.192.1-24.bl.2.4
24.a4 24.a \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $[0, -1, 0, -4, 4]$ \(y^2=x^3-x^2-4x+4\) 2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.h.1.6, 12.48.0-12.c.1.1, 24.192.1-24.bu.1.7
24.a5 24.a \( 2^{3} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $[0, -1, 0, 1, 0]$ \(y^2=x^3-x^2+x\) 2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 8.48.0-8.ba.1.2, 12.24.0-12.g.1.2, $\ldots$
24.a6 24.a \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $[0, -1, 0, 16, -180]$ \(y^2=x^3-x^2+16x-180\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.96.0-8.m.1.2, 48.192.1-48.w.2.4
26.a1 26.a \( 2 \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 0, 1, -460, -3830]$ \(y^2+xy+y=x^3-460x-3830\) 3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$
26.a2 26.a \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $[1, 0, 1, -5, -8]$ \(y^2+xy+y=x^3-5x-8\) 3.24.0-3.a.1.1, 104.2.0.?, 117.72.0.?, 312.48.1.?, 936.144.3.?
26.a3 26.a \( 2 \cdot 13 \) $0$ $\Z/3\Z$ $1$ $[1, 0, 1, 0, 0]$ \(y^2+xy+y=x^3\) 3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$
26.b1 26.b \( 2 \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, -1, 1, -213, -1257]$ \(y^2+xy+y=x^3-x^2-213x-1257\) 7.48.0-7.a.2.2, 104.2.0.?, 728.96.2.?
26.b2 26.b \( 2 \cdot 13 \) $0$ $\Z/7\Z$ $1$ $[1, -1, 1, -3, 3]$ \(y^2+xy+y=x^3-x^2-3x+3\) 7.48.0-7.a.1.2, 104.2.0.?, 728.96.2.?
27.a1 27.a \( 3^{3} \) $0$ $\mathsf{trivial}$ $-27$ $1$ $[0, 0, 1, -270, -1708]$ \(y^2+y=x^3-270x-1708\)
27.a2 27.a \( 3^{3} \) $0$ $\Z/3\Z$ $-27$ $1$ $[0, 0, 1, -30, 63]$ \(y^2+y=x^3-30x+63\)
27.a3 27.a \( 3^{3} \) $0$ $\Z/3\Z$ $-3$ $1$ $[0, 0, 1, 0, -7]$ \(y^2+y=x^3-7\)
27.a4 27.a \( 3^{3} \) $0$ $\Z/3\Z$ $-3$ $1$ $[0, 0, 1, 0, 0]$ \(y^2+y=x^3\)
30.a1 30.a \( 2 \cdot 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -5334, -150368]$ \(y^2+xy+y=x^3-5334x-150368\) 2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.3, $\ldots$
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