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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images
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.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.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, $\ldots$
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, $\ldots$
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.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.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.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, $\ldots$
30.a3 30.a \( 2 \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -334, -2368]$ \(y^2+xy+y=x^3-334x-2368\) 2.6.0.a.1, 3.8.0-3.a.1.1, 6.48.0-6.a.1.2, 8.12.0-2.a.1.1, 12.96.0-12.a.1.15, $\ldots$
32.a2 32.a \( 2^{5} \) $0$ $\Z/4\Z$ $-16$ $1$ $[0, 0, 0, -11, 14]$ \(y^2=x^3-11x+14\)
32.a3 32.a \( 2^{5} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $1$ $[0, 0, 0, -1, 0]$ \(y^2=x^3-x\)
32.a4 32.a \( 2^{5} \) $0$ $\Z/4\Z$ $-4$ $1$ $[0, 0, 0, 4, 0]$ \(y^2=x^3+4x\)
33.a1 33.a \( 3 \cdot 11 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 0, -146, 621]$ \(y^2+xy=x^3+x^2-146x+621\) 2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 88.24.0.?, 264.48.0.?
33.a2 33.a \( 3 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -11, 0]$ \(y^2+xy=x^3+x^2-11x\) 2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 44.24.0-44.b.1.2, 132.48.0.?
39.a2 39.a \( 3 \cdot 13 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 0, -19, 22]$ \(y^2+xy=x^3+x^2-19x+22\) 2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 104.24.0.?, 312.48.0.?
39.a3 39.a \( 3 \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -4, -5]$ \(y^2+xy=x^3+x^2-4x-5\) 2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 52.24.0-52.b.1.2, 156.48.0.?
40.a2 40.a \( 2^{3} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[0, 0, 0, -7, -6]$ \(y^2=x^3-7x-6\) 2.6.0.a.1, 4.24.0-4.a.1.1, 8.48.0-8.g.1.1, 20.48.0-20.b.1.1, 40.192.3-40.bk.1.5
40.a3 40.a \( 2^{3} \cdot 5 \) $0$ $\Z/4\Z$ $1$ $[0, 0, 0, -2, 1]$ \(y^2=x^3-2x+1\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 10.6.0.a.1, 16.48.0-16.i.1.1, $\ldots$
40.a4 40.a \( 2^{3} \cdot 5 \) $0$ $\Z/4\Z$ $1$ $[0, 0, 0, 13, -34]$ \(y^2=x^3+13x-34\) 2.3.0.a.1, 4.48.0-4.c.1.1, 40.96.1-40.dk.1.1, 80.192.3.?
42.a1 42.a \( 2 \cdot 3 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 1, -1344, 18405]$ \(y^2+xy+y=x^3+x^2-1344x+18405\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 16.96.0-16.z.2.3, 28.24.0-28.h.1.2, $\ldots$
42.a3 42.a \( 2 \cdot 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 1, -104, 101]$ \(y^2+xy+y=x^3+x^2-104x+101\) 2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.f.1.1, 56.192.1-56.bp.2.4
45.a2 45.a \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -1215, 16600]$ \(y^2+xy=x^3-x^2-1215x+16600\) 2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 12.24.0-4.b.1.1, 16.96.0-8.k.1.2, $\ldots$
45.a5 45.a \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -90, 175]$ \(y^2+xy=x^3-x^2-90x+175\) 2.6.0.a.1, 4.24.0.b.1, 8.96.0-8.b.2.6, 12.48.0-4.b.1.1, 24.192.1-24.n.1.8, $\ldots$
45.a6 45.a \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -45, -104]$ \(y^2+xy=x^3-x^2-45x-104\) 2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.6, 12.24.0-4.b.1.3, 16.96.0-16.d.2.4, $\ldots$
48.a1 48.a \( 2^{4} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $[0, 1, 0, -384, 2772]$ \(y^2=x^3+x^2-384x+2772\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.r.1.2, 16.96.0-16.l.1.2, 24.96.0-24.bf.1.8, $\ldots$
48.a4 48.a \( 2^{4} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[0, 1, 0, -4, -4]$ \(y^2=x^3+x^2-4x-4\) 2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.h.1.2, 12.48.0-12.c.1.3, 24.192.1-24.bu.1.1
55.a1 55.a \( 5 \cdot 11 \) $0$ $\Z/4\Z$ $1$ $[1, -1, 0, -59, 190]$ \(y^2+xy=x^3-x^2-59x+190\) 2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 44.24.0-44.h.1.2, 440.48.0.?
55.a3 55.a \( 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -4, 3]$ \(y^2+xy=x^3-x^2-4x+3\) 2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 44.24.0-44.a.1.1, 220.48.0.?
56.a3 56.a \( 2^{3} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[0, 0, 0, -19, 30]$ \(y^2=x^3-19x+30\) 2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 28.24.0-28.b.1.1, 56.48.0-56.d.1.3
56.a4 56.a \( 2^{3} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $[0, 0, 0, 1, 2]$ \(y^2=x^3+x+2\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, $\ldots$
57.c1 57.c \( 3 \cdot 19 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 1, -102, 385]$ \(y^2+xy+y=x^3-102x+385\) 2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 76.24.0.?, 456.48.0.?
57.c2 57.c \( 3 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -7, 5]$ \(y^2+xy+y=x^3-7x+5\) 2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 76.24.0.?, 228.48.0.?
62.a3 62.a \( 2 \cdot 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 1, -21, 41]$ \(y^2+xy+y=x^3-x^2-21x+41\) 2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 124.24.0.?, 248.48.0.?
62.a4 62.a \( 2 \cdot 31 \) $0$ $\Z/4\Z$ $1$ $[1, -1, 1, -1, 1]$ \(y^2+xy+y=x^3-x^2-x+1\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 62.6.0.b.1, 124.24.0.?, $\ldots$
63.a1 63.a \( 3^{2} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $[1, -1, 0, -7056, 229905]$ \(y^2+xy=x^3-x^2-7056x+229905\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 12.24.0-12.h.1.2, 16.48.0-16.e.2.10, $\ldots$
63.a2 63.a \( 3^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -441, 3672]$ \(y^2+xy=x^3-x^2-441x+3672\) 2.6.0.a.1, 4.24.0-4.b.1.2, 8.48.0-8.e.1.8, 12.48.0-12.c.1.2, 24.96.0-24.j.2.4, $\ldots$
63.a5 63.a \( 3^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -36, 27]$ \(y^2+xy=x^3-x^2-36x+27\) 2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.e.2.6, 12.24.0-4.b.1.3, 24.96.0-24.w.2.1, $\ldots$
64.a2 64.a \( 2^{6} \) $0$ $\Z/4\Z$ $-16$ $1$ $[0, 0, 0, -44, 112]$ \(y^2=x^3-44x+112\)
64.a3 64.a \( 2^{6} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $1$ $[0, 0, 0, -4, 0]$ \(y^2=x^3-4x\)
66.b2 66.b \( 2 \cdot 3 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 1, -22, -49]$ \(y^2+xy+y=x^3+x^2-22x-49\) 2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 132.24.0.?, 264.48.0.?
66.b4 66.b \( 2 \cdot 3 \cdot 11 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 1, -2, -1]$ \(y^2+xy+y=x^3+x^2-2x-1\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 66.6.0.a.1, 132.24.0.?, $\ldots$
70.a3 70.a \( 2 \cdot 5 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 1, -18, -19]$ \(y^2+xy+y=x^3-x^2-18x-19\) 2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 28.24.0-28.b.1.1, 56.48.0-56.d.1.3
70.a4 70.a \( 2 \cdot 5 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $[1, -1, 1, 2, -3]$ \(y^2+xy+y=x^3-x^2+2x-3\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, $\ldots$
72.a3 72.a \( 2^{3} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[0, 0, 0, -219, 1190]$ \(y^2=x^3-219x+1190\) 2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.e.2.4, 12.24.0-4.b.1.1, 24.192.1-24.bl.2.1
72.a4 72.a \( 2^{3} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[0, 0, 0, -39, -70]$ \(y^2=x^3-39x-70\) 2.6.0.a.1, 4.24.0-4.b.1.2, 8.96.0-8.h.1.7, 12.48.0-12.c.1.4, 24.192.1-24.bu.1.2
72.a5 72.a \( 2^{3} \cdot 3^{2} \) $0$ $\Z/4\Z$ $1$ $[0, 0, 0, 6, -7]$ \(y^2=x^3+6x-7\) 2.3.0.a.1, 4.12.0-4.c.1.1, 6.6.0.a.1, 8.48.0-8.ba.1.7, 12.24.0-12.g.1.2, $\ldots$
75.b2 75.b \( 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -3376, -75727]$ \(y^2+xy+y=x^3-3376x-75727\) 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, $\ldots$
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