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Properties

Label 147294d
Number of curves $2$
Conductor $147294$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 147294d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
147294.bj2 147294d1 \([1, -1, 1, -54032, 5315055]\) \(-203401212841/23861628\) \(-2046519274304988\) \([2]\) \(1474560\) \(1.6739\) \(\Gamma_0(N)\)-optimal
147294.bj1 147294d2 \([1, -1, 1, -887522, 322041255]\) \(901456690969801/10542042\) \(904150049759082\) \([2]\) \(2949120\) \(2.0204\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 147294.2.a.d

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