Properties

Label 91728.gb
Number of curves $2$
Conductor $91728$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gb1")
 
E.isogeny_class()
 

Elliptic curves in class 91728.gb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91728.gb1 91728c1 \([0, 0, 0, -4263, -106330]\) \(10536048/91\) \(74000279808\) \([2]\) \(172032\) \(0.90999\) \(\Gamma_0(N)\)-optimal
91728.gb2 91728c2 \([0, 0, 0, -1323, -250390]\) \(-78732/8281\) \(-26936101850112\) \([2]\) \(344064\) \(1.2566\)  

Rank

sage: E.rank()
 

The elliptic curves in class 91728.gb have rank \(0\).

Complex multiplication

The elliptic curves in class 91728.gb do not have complex multiplication.

Modular form 91728.2.a.gb

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} - 4 q^{11} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.