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Properties

Label 24150bm
Number of curves $2$
Conductor $24150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 24150bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bp2 24150bm1 \([1, 1, 1, -4813, -127969]\) \(789145184521/17996580\) \(281196562500\) \([2]\) \(46080\) \(0.98346\) \(\Gamma_0(N)\)-optimal
24150.bp1 24150bm2 \([1, 1, 1, -10563, 228531]\) \(8341959848041/3327411150\) \(51990799218750\) \([2]\) \(92160\) \(1.3300\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150bm have rank \(0\).

Complex multiplication

The elliptic curves in class 24150bm do not have complex multiplication.

Modular form 24150.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 2 q^{11} - q^{12} + 2 q^{13} - q^{14} + q^{16} + q^{18} - 6 q^{19} + O(q^{20})\) 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.