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Properties

Label 24882.e
Number of curves $2$
Conductor $24882$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 24882.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24882.e1 24882a2 \([1, 1, 0, -33410, -2364336]\) \(4124520340578627625/312462035028\) \(312462035028\) \([2]\) \(71680\) \(1.2545\)  
24882.e2 24882a1 \([1, 1, 0, -1950, -42588]\) \(-820683103515625/278985543408\) \(-278985543408\) \([2]\) \(35840\) \(0.90793\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24882.e have rank \(1\).

Complex multiplication

The elliptic curves in class 24882.e do not have complex multiplication.

Modular form 24882.2.a.e

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