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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4018.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4018.d1 | 4018h2 | \([1, 0, 1, -108855, -10335622]\) | \(1212480836738137/310100175392\) | \(36482975534693408\) | \([2]\) | \(46080\) | \(1.8874\) | |
4018.d2 | 4018h1 | \([1, 0, 1, -101015, -12364614]\) | \(968917714969177/100803584\) | \(11859440854016\) | \([2]\) | \(23040\) | \(1.5409\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4018.d have rank \(1\).
Complex multiplication
The elliptic curves in class 4018.d do not have complex multiplication.Modular form 4018.2.a.d
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 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.