Properties

Label 187200io
Number of curves 22
Conductor 187200187200
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("io1")
 
E.isogeny_class()
 

Elliptic curves in class 187200io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.y2 187200io1 [0,0,0,172500,594110000][0, 0, 0, 172500, 594110000] 7604375/20470327604375/2047032 152810119987200000000-152810119987200000000 [][] 49766404976640 2.55222.5522 Γ0(N)\Gamma_0(N)-optimal
187200.y1 187200io2 [0,0,0,48427500,129734030000][0, 0, 0, -48427500, 129734030000] 168256703745625/30371328-168256703745625/30371328 2267207486668800000000-2267207486668800000000 [][] 1492992014929920 3.10153.1015  

Rank

sage: E.rank()
 

The elliptic curves in class 187200io have rank 11.

Complex multiplication

The elliptic curves in class 187200io do not have complex multiplication.

Modular form 187200.2.a.io

sage: E.q_eigenform(10)
 
q4q7q135q19+O(q20)q - 4 q^{7} - q^{13} - 5 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.