Properties

Label 350064bc
Number of curves $2$
Conductor $350064$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 350064bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.bc1 350064bc1 \([0, 0, 0, -434955, -100427078]\) \(3047678972871625/304559880768\) \(909410931015155712\) \([2]\) \(4128768\) \(2.1823\) \(\Gamma_0(N)\)-optimal
350064.bc2 350064bc2 \([0, 0, 0, 538485, -486104006]\) \(5783051584712375/37533175779528\) \(-112073462346858135552\) \([2]\) \(8257536\) \(2.5289\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350064bc have rank \(0\).

Complex multiplication

The elliptic curves in class 350064bc do not have complex multiplication.

Modular form 350064.2.a.bc

sage: E.q_eigenform(10)
 
\(q - 2q^{7} + q^{11} + q^{13} + q^{17} - 4q^{19} + O(q^{20})\)  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.