Properties

Label 35904.ba
Number of curves $2$
Conductor $35904$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35904.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35904.ba1 35904q1 \([0, -1, 0, -57857, 5333505]\) \(81706955619457/744505344\) \(195167608897536\) \([2]\) \(215040\) \(1.5643\) \(\Gamma_0(N)\)-optimal
35904.ba2 35904q2 \([0, -1, 0, -16897, 12698113]\) \(-2035346265217/264305213568\) \(-69286025905569792\) \([2]\) \(430080\) \(1.9109\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35904.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 35904.ba do not have complex multiplication.

Modular form 35904.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} - 4q^{7} + q^{9} + q^{11} + 4q^{13} - 2q^{15} - q^{17} + 8q^{19} + O(q^{20})\)  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.