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Properties

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

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 24150cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.cn2 24150cm1 \([1, 0, 0, 8337, 677817]\) \(4101378352343/15049939968\) \(-235155312000000\) \([2]\) \(122880\) \(1.4405\) \(\Gamma_0(N)\)-optimal
24150.cn1 24150cm2 \([1, 0, 0, -83663, 8129817]\) \(4144806984356137/568114785504\) \(8876793523500000\) \([2]\) \(245760\) \(1.7871\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24150.2.a.cm

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