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Properties

Label 61347.f
Number of curves $2$
Conductor $61347$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 61347.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61347.f1 61347m2 \([1, 1, 1, -1534101, 4065656772]\) \(-276301129/4782969\) \(-6911948529702589033089\) \([]\) \(3057600\) \(2.8718\)  
61347.f2 61347m1 \([1, 1, 1, -204916, -36208138]\) \(-658489/9\) \(-13006050586429329\) \([]\) \(436800\) \(1.8988\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 61347.f have rank \(0\).

Complex multiplication

The elliptic curves in class 61347.f do not have complex multiplication.

Modular form 61347.2.a.f

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.