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Properties

Label 147994.e
Number of curves $2$
Conductor $147994$
CM no
Rank $0$
Graph

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

Elliptic curves in class 147994.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
147994.e1 147994v2 \([1, 0, 1, -225375, 41162966]\) \(1426487591593/2156\) \(1913457936236\) \([2]\) \(887040\) \(1.6247\)  
147994.e2 147994v1 \([1, 0, 1, -13955, 654894]\) \(-338608873/13552\) \(-12027449884912\) \([2]\) \(443520\) \(1.2781\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 147994.e have rank \(0\).

Complex multiplication

The elliptic curves in class 147994.e do not have complex multiplication.

Modular form 147994.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} - q^{11} - 2 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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 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.