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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 13923l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13923.k1 | 13923l1 | \([1, -1, 0, -4095, -99792]\) | \(10418796526321/6390657\) | \(4658788953\) | \([2]\) | \(17920\) | \(0.79795\) | \(\Gamma_0(N)\)-optimal |
13923.k2 | 13923l2 | \([1, -1, 0, -3330, -138807]\) | \(-5602762882081/8312741073\) | \(-6059988242217\) | \([2]\) | \(35840\) | \(1.1445\) |
Rank
sage: E.rank()
The elliptic curves in class 13923l have rank \(0\).
Complex multiplication
The elliptic curves in class 13923l do not have complex multiplication.Modular form 13923.2.a.l
sage: E.q_eigenform(10)
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.