Properties

Label 10608a
Number of curves $2$
Conductor $10608$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 10608a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10608.e2 10608a1 \([0, -1, 0, -40108, 3053056]\) \(27873248949250000/538367795433\) \(137822155630848\) \([2]\) \(36864\) \(1.5059\) \(\Gamma_0(N)\)-optimal
10608.e1 10608a2 \([0, -1, 0, -84048, -4785840]\) \(64122592551794500/27331783704693\) \(27987746513605632\) \([2]\) \(73728\) \(1.8525\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10608a have rank \(0\).

Complex multiplication

The elliptic curves in class 10608a do not have complex multiplication.

Modular form 10608.2.a.a

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