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Properties

Label 54150bl
Number of curves $2$
Conductor $54150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 54150bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.bx2 54150bl1 \([1, 1, 1, -7313, 232031]\) \(403583419/10800\) \(1157456250000\) \([2]\) \(92160\) \(1.0955\) \(\Gamma_0(N)\)-optimal
54150.bx1 54150bl2 \([1, 1, 1, -16813, -508969]\) \(4904335099/1822500\) \(195320742187500\) \([2]\) \(184320\) \(1.4421\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54150bl have rank \(0\).

Complex multiplication

The elliptic curves in class 54150bl do not have complex multiplication.

Modular form 54150.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 2 q^{11} - q^{12} - 4 q^{13} + q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.