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Properties

Label 24150.m
Number of curves $2$
Conductor $24150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.m1 24150n2 \([1, 1, 0, -5750, 162750]\) \(1345938541921/24850350\) \(388286718750\) \([2]\) \(36864\) \(1.0183\)  
24150.m2 24150n1 \([1, 1, 0, 0, 7500]\) \(-1/1555260\) \(-24300937500\) \([2]\) \(18432\) \(0.67170\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24150.m have rank \(1\).

Complex multiplication

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

Modular form 24150.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} - q^{14} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.