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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.k1 24150u1 \([1, 1, 0, -345, 2325]\) \(36495256013/54096\) \(6762000\) \([2]\) \(9216\) \(0.21163\) \(\Gamma_0(N)\)-optimal
24150.k2 24150u2 \([1, 1, 0, -245, 3825]\) \(-13094193293/45724644\) \(-5715580500\) \([2]\) \(18432\) \(0.55821\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150.k have rank \(2\).

Complex multiplication

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

Modular form 24150.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 4 q^{11} - q^{12} - 4 q^{13} - q^{14} + q^{16} - 4 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.