Properties

Label 3450.p
Number of curves $4$
Conductor $3450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3450.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.p1 3450o3 \([1, 1, 1, -266088, 52603281]\) \(133345896593725369/340006815000\) \(5312606484375000\) \([2]\) \(46080\) \(1.8939\)  
3450.p2 3450o2 \([1, 1, 1, -23088, 115281]\) \(87109155423289/49979073600\) \(780923025000000\) \([2, 2]\) \(23040\) \(1.5473\)  
3450.p3 3450o1 \([1, 1, 1, -15088, -716719]\) \(24310870577209/114462720\) \(1788480000000\) \([2]\) \(11520\) \(1.2007\) \(\Gamma_0(N)\)-optimal
3450.p4 3450o4 \([1, 1, 1, 91912, 1035281]\) \(5495662324535111/3207841648920\) \(-50122525764375000\) \([2]\) \(46080\) \(1.8939\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3450.2.a.p

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.