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Properties

Label 24150.x
Number of curves $4$
Conductor $24150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.x1 24150bd4 \([1, 0, 1, -112276, -14489302]\) \(10017490085065009/235066440\) \(3672913125000\) \([2]\) \(147456\) \(1.5230\)  
24150.x2 24150bd3 \([1, 0, 1, -30276, 1814698]\) \(196416765680689/22365315000\) \(349458046875000\) \([2]\) \(147456\) \(1.5230\)  
24150.x3 24150bd2 \([1, 0, 1, -7276, -209302]\) \(2725812332209/373262400\) \(5832225000000\) \([2, 2]\) \(73728\) \(1.1764\)  
24150.x4 24150bd1 \([1, 0, 1, 724, -17302]\) \(2691419471/9891840\) \(-154560000000\) \([2]\) \(36864\) \(0.82986\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24150.2.a.x

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.