Properties

Label 3450.t
Number of curves $2$
Conductor $3450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3450.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.t1 3450u2 \([1, 0, 0, -18838, -442708]\) \(47316161414809/22001657400\) \(343775896875000\) \([2]\) \(16128\) \(1.4838\)  
3450.t2 3450u1 \([1, 0, 0, 4162, -51708]\) \(510273943271/370215360\) \(-5784615000000\) \([2]\) \(8064\) \(1.1372\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3450.t have rank \(1\).

Complex multiplication

The elliptic curves in class 3450.t do not have complex multiplication.

Modular form 3450.2.a.t

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