Properties

Label 91035.ba
Number of curves $3$
Conductor $91035$
CM no
Rank $0$
Graph

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

Elliptic curves in class 91035.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.ba1 91035d3 \([0, 0, 1, -341598, 80387734]\) \(-250523582464/13671875\) \(-240574247279296875\) \([]\) \(907200\) \(2.0934\)  
91035.ba2 91035d1 \([0, 0, 1, -3468, -87206]\) \(-262144/35\) \(-615870073035\) \([]\) \(100800\) \(0.99476\) \(\Gamma_0(N)\)-optimal
91035.ba3 91035d2 \([0, 0, 1, 22542, 222313]\) \(71991296/42875\) \(-754440839467875\) \([]\) \(302400\) \(1.5441\)  

Rank

sage: E.rank()
 

The elliptic curves in class 91035.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 91035.ba do not have complex multiplication.

Modular form 91035.2.a.ba

sage: E.q_eigenform(10)
 
\(q - 2q^{4} - q^{5} - q^{7} - 3q^{11} + 5q^{13} + 4q^{16} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.