Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 91035.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.z1 91035f2 \([0, 0, 1, -32203848, 70341200734]\) \(-209906535145406464/6559875\) \(-115429448438584875\) \([]\) \(3649536\) \(2.7778\)  
91035.z2 91035f1 \([0, 0, 1, -367608, 111649153]\) \(-312217698304/125355195\) \(-2205786088570476195\) \([]\) \(1216512\) \(2.2285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 91035.2.a.z

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} - q^{7} - 6 q^{11} - q^{13} + 4 q^{16} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.