Properties

Label 91035.r
Number of curves $2$
Conductor $91035$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 91035.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.r1 91035bh2 \([1, -1, 1, -3253688492, 63270172598784]\) \(216486375407331255135001/27004994294227023375\) \(475187651665581576138054348375\) \([2]\) \(92897280\) \(4.4241\)  
91035.r2 91035bh1 \([1, -1, 1, 301553383, 5117792297784]\) \(172343644217341694999/742780064187984375\) \(-13070171782297026428591109375\) \([2]\) \(46448640\) \(4.0775\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 91035.r have rank \(1\).

Complex multiplication

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

Modular form 91035.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} - q^{7} + 3 q^{8} - q^{10} + 4 q^{13} + q^{14} - q^{16} + 2 q^{19} + O(q^{20})\) 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.