Properties

Label 35280.bs
Number of curves $4$
Conductor $35280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 35280.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.bs1 35280z4 \([0, 0, 0, -1647723, 814091978]\) \(5633270409316/14175\) \(1244912399539200\) \([2]\) \(393216\) \(2.1347\)  
35280.bs2 35280z3 \([0, 0, 0, -289443, -43871758]\) \(30534944836/8203125\) \(720435416400000000\) \([2]\) \(393216\) \(2.1347\)  
35280.bs3 35280z2 \([0, 0, 0, -104223, 12398078]\) \(5702413264/275625\) \(6051657497760000\) \([2, 2]\) \(196608\) \(1.7882\)  
35280.bs4 35280z1 \([0, 0, 0, 3822, 750827]\) \(4499456/180075\) \(-247109347825200\) \([2]\) \(98304\) \(1.4416\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35280.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 35280.bs do not have complex multiplication.

Modular form 35280.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.