Properties

Label 91035.bi
Number of curves $4$
Conductor $91035$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 91035.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.bi1 91035h4 \([1, -1, 0, -4385340, -3533456039]\) \(530044731605089/26309115\) \(462942759329606115\) \([2]\) \(2359296\) \(2.4611\)  
91035.bi2 91035h3 \([1, -1, 0, -1394190, 589363051]\) \(17032120495489/1339001685\) \(23561459015283944685\) \([2]\) \(2359296\) \(2.4611\)  
91035.bi3 91035h2 \([1, -1, 0, -288765, -48909344]\) \(151334226289/28676025\) \(504591588888671025\) \([2, 2]\) \(1179648\) \(2.1145\)  
91035.bi4 91035h1 \([1, -1, 0, 36360, -4497269]\) \(302111711/669375\) \(-11778515146794375\) \([2]\) \(589824\) \(1.7679\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 91035.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} - q^{7} - 3 q^{8} - q^{10} - 6 q^{13} - q^{14} - q^{16} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.