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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 106470.es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106470.es1 | 106470dk1 | \([1, -1, 1, -865988, 309727591]\) | \(551105805571803/1376829440\) | \(179433703776337920\) | \([2]\) | \(2150400\) | \(2.1881\) | \(\Gamma_0(N)\)-optimal |
106470.es2 | 106470dk2 | \([1, -1, 1, -541508, 544391527]\) | \(-134745327251163/903920796800\) | \(-117802432006598102400\) | \([2]\) | \(4300800\) | \(2.5347\) |
Rank
sage: E.rank()
The elliptic curves in class 106470.es have rank \(1\).
Complex multiplication
The elliptic curves in class 106470.es do not have complex multiplication.Modular form 106470.2.a.es
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.