Properties

Label 91035.w
Number of curves $2$
Conductor $91035$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 91035.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.w1 91035bs2 \([1, -1, 1, -201632, 34774724]\) \(51520374361/212415\) \(3737715473249415\) \([2]\) \(589824\) \(1.8435\)  
91035.w2 91035bs1 \([1, -1, 1, -6557, 1065764]\) \(-1771561/26775\) \(-471140605871775\) \([2]\) \(294912\) \(1.4969\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 91035.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + q^{7} + 3 q^{8} - q^{10} - q^{14} - q^{16} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.