Properties

Label 46200bl
Number of curves $4$
Conductor $46200$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46200bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.de4 46200bl1 \([0, 1, 0, 9092, 322688]\) \(20777545136/23059575\) \(-92238300000000\) \([2]\) \(98304\) \(1.3661\) \(\Gamma_0(N)\)-optimal
46200.de3 46200bl2 \([0, 1, 0, -51408, 2984688]\) \(939083699236/300155625\) \(4802490000000000\) \([2, 2]\) \(196608\) \(1.7127\)  
46200.de2 46200bl3 \([0, 1, 0, -326408, -69615312]\) \(120186986927618/4332064275\) \(138626056800000000\) \([2]\) \(393216\) \(2.0593\)  
46200.de1 46200bl4 \([0, 1, 0, -744408, 246920688]\) \(1425631925916578/270703125\) \(8662500000000000\) \([2]\) \(393216\) \(2.0593\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46200bl have rank \(0\).

Complex multiplication

The elliptic curves in class 46200bl do not have complex multiplication.

Modular form 46200.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.