Properties

Label 10830.d
Number of curves $2$
Conductor $10830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 10830.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.d1 10830d2 \([1, 1, 0, -8420693, 9401731647]\) \(1403607530712116449/39475350\) \(1857152618533350\) \([2]\) \(403200\) \(2.4403\)  
10830.d2 10830d1 \([1, 1, 0, -525623, 147130593]\) \(-341370886042369/1817528220\) \(-85507216352261820\) \([2]\) \(201600\) \(2.0937\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10830.d have rank \(0\).

Complex multiplication

The elliptic curves in class 10830.d do not have complex multiplication.

Modular form 10830.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} + O(q^{20})\) 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.