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Properties

Label 35574cf
Number of curves $2$
Conductor $35574$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 35574cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.bn2 35574cf1 \([1, 1, 1, 139208, -24461095]\) \(596183/864\) \(-432364724288947296\) \([]\) \(567000\) \(2.0695\) \(\Gamma_0(N)\)-optimal
35574.bn1 35574cf2 \([1, 1, 1, -4218607, -3353831755]\) \(-16591834777/98304\) \(-49193497519098003456\) \([]\) \(1701000\) \(2.6188\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35574cf have rank \(0\).

Complex multiplication

The elliptic curves in class 35574cf do not have complex multiplication.

Modular form 35574.2.a.cf

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.