Properties

Label 14350b
Number of curves $2$
Conductor $14350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 14350b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14350.i2 14350b1 \([1, -1, 0, -483817, 119355341]\) \(801581275315909089/70810888830976\) \(1106420137984000000\) \([]\) \(493920\) \(2.2025\) \(\Gamma_0(N)\)-optimal
14350.i1 14350b2 \([1, -1, 0, -240282817, -1433553773659]\) \(98191033604529537629349729/10906239337336\) \(170409989645875000\) \([]\) \(3457440\) \(3.1755\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14350b have rank \(1\).

Complex multiplication

The elliptic curves in class 14350b do not have complex multiplication.

Modular form 14350.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} - 3 q^{6} - q^{7} - q^{8} + 6 q^{9} - 2 q^{11} + 3 q^{12} + q^{14} + q^{16} + 3 q^{17} - 6 q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.