Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 91035u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.bl2 91035u1 \([1, -1, 0, 2326019625, 178302165067336]\) \(16098893047132187167/168182866341984375\) \(-14539503308369857195506322359375\) \([2]\) \(137871360\) \(4.6606\) \(\Gamma_0(N)\)-optimal
91035.bl1 91035u2 \([1, -1, 0, -36838524870, 2527477705875325]\) \(63953244990201015504593/5088175635498046875\) \(439875643072107929613071044921875\) \([2]\) \(275742720\) \(5.0072\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 91035.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} + q^{7} - 3 q^{8} - q^{10} + 2 q^{11} + 2 q^{13} + q^{14} - q^{16} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.