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Properties

Label 134310.d
Number of curves $2$
Conductor $134310$
CM no
Rank $1$
Graph

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

Elliptic curves in class 134310.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134310.d1 134310cp1 \([1, 1, 0, -40053, -1468947]\) \(4011342040369/1807080000\) \(3201352451880000\) \([2]\) \(921600\) \(1.6705\) \(\Gamma_0(N)\)-optimal
134310.d2 134310cp2 \([1, 1, 0, 139027, -10816923]\) \(167749090607951/125915625000\) \(-223067210540625000\) \([2]\) \(1843200\) \(2.0170\)  

Rank

sage: E.rank()
 

The elliptic curves in class 134310.d have rank \(1\).

Complex multiplication

The elliptic curves in class 134310.d do not have complex multiplication.

Modular form 134310.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} - q^{12} + 2 q^{13} + 2 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.