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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 8470.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.v1 | 8470bg2 | \([1, 0, 0, -102550, -12089868]\) | \(67324767141241/3368750000\) | \(5967946118750000\) | \([2]\) | \(61440\) | \(1.7858\) | |
8470.v2 | 8470bg1 | \([1, 0, 0, 3930, -739100]\) | \(3789119879/135520000\) | \(-240081946720000\) | \([2]\) | \(30720\) | \(1.4393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8470.v have rank \(1\).
Complex multiplication
The elliptic curves in class 8470.v do not have complex multiplication.Modular form 8470.2.a.v
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.