# given a curve this spits out lots of data
K.<a> = NumberField(x^2 - x - 1)
E = EllipticCurve(K, [a,a+1,a,2*a,a]);
var = E.simon_two_descent()
tor = E.two_torsion_rank(); print var[1] - tor;
c = E.conductor();
print c;
print norm(c);
D = E.discriminant();
j = E.j_invariant(); d = j.denominator_ideal();
pa = K.primes_above(d)
print len(E.torsion_subgroup())
v = K.embeddings(RR);
print v[0](D);
print v[1](D);
for i in range(len(pa)):
print D.valuation(pa[i])
for i in range(len(pa)):
print d.valuation(pa[i])
for i in range(len(pa)):
print E.tamagawa_number(pa[i])
for i in range(len(pa)):
print E.kodaira_symbol(pa[i])
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0
Fractional ideal (2*a - 11)
95
6
37.8115294937453
-62.8115294937453
3
1
3
1
3
1
I3
I1
0
Fractional ideal (2*a - 11)
95
6
37.8115294937453
-62.8115294937453
3
1
3
1
3
1
I3
I1
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