Properties

Label 3450.z
Number of curves $2$
Conductor $3450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3450.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.z1 3450v2 \([1, 0, 0, -79301438, -268415348508]\) \(3529773792266261468365081/50841342773437500000\) \(794395980834960937500000\) \([2]\) \(829440\) \(3.3900\)  
3450.z2 3450v1 \([1, 0, 0, -569438, -11355368508]\) \(-1306902141891515161/3564268498800000000\) \(-55691695293750000000000\) \([2]\) \(414720\) \(3.0435\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3450.z have rank \(0\).

Complex multiplication

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

Modular form 3450.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} + 2q^{13} + 2q^{14} + q^{16} + q^{18} + 8q^{19} + O(q^{20})\)  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 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.