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Properties

Label 24150e
Number of curves $2$
Conductor $24150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 24150e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.d2 24150e1 \([1, 1, 0, 75, 1125]\) \(2924207/34776\) \(-543375000\) \([]\) \(12960\) \(0.35701\) \(\Gamma_0(N)\)-optimal
24150.d1 24150e2 \([1, 1, 0, -675, -31125]\) \(-2181825073/25039686\) \(-391245093750\) \([]\) \(38880\) \(0.90632\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24150.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - q^{12} - 5 q^{13} + q^{14} + q^{16} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.