Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3450.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.u1 3450y2 \([1, 0, 0, -6063, -182133]\) \(1577505447721/838350\) \(13099218750\) \([2]\) \(6912\) \(0.89107\)  
3450.u2 3450y1 \([1, 0, 0, -313, -3883]\) \(-217081801/285660\) \(-4463437500\) \([2]\) \(3456\) \(0.54449\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3450.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} - 4q^{13} - 4q^{14} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20})\)  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 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.