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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 106470v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106470.n2 | 106470v1 | \([1, -1, 0, -5355, 39950145]\) | \(-169/6860\) | \(-689422046227338060\) | \([]\) | \(1797120\) | \(2.1018\) | \(\Gamma_0(N)\)-optimal |
106470.n1 | 106470v2 | \([1, -1, 0, -9002070, 10398767796]\) | \(-802767616729/56000\) | \(-5627935071243576000\) | \([]\) | \(5391360\) | \(2.6511\) |
Rank
sage: E.rank()
The elliptic curves in class 106470v have rank \(0\).
Complex multiplication
The elliptic curves in class 106470v do not have complex multiplication.Modular form 106470.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.