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Properties

Label 348082.f
Number of curves $2$
Conductor $348082$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 348082.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348082.f1 348082f2 \([1, -1, 0, -6361853, 6016304709]\) \(192356835606793593/5746104240128\) \(850629649474017953792\) \([2]\) \(17842176\) \(2.7928\)  
348082.f2 348082f1 \([1, -1, 0, -944893, -220783035]\) \(630238383410553/222168088576\) \(32888850499778904064\) \([2]\) \(8921088\) \(2.4462\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 348082.f have rank \(1\).

Complex multiplication

The elliptic curves in class 348082.f do not have complex multiplication.

Modular form 348082.2.a.f

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