Properties

Label 147294.v
Number of curves $2$
Conductor $147294$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 147294.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
147294.v1 147294ck2 \([1, -1, 0, -29556, -1278936]\) \(33293019313/10932488\) \(937637088639048\) \([2]\) \(829440\) \(1.5759\)  
147294.v2 147294ck1 \([1, -1, 0, -11916, 488592]\) \(2181825073/74816\) \(6416678108736\) \([2]\) \(414720\) \(1.2293\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 147294.v have rank \(0\).

Complex multiplication

The elliptic curves in class 147294.v do not have complex multiplication.

Modular form 147294.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - q^{8} - 2 q^{10} - 4 q^{11} + 6 q^{13} + q^{16} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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.