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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 60690.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60690.f1 | 60690l2 | \([1, 1, 0, -118828773, -498624543603]\) | \(37769548376817211811066153/1011738331054080\) | \(4970670420468695040\) | \([2]\) | \(8847360\) | \(3.1010\) | |
60690.f2 | 60690l1 | \([1, 1, 0, -7417573, -7813643123]\) | \(-9186763300983704416553/47730830553907200\) | \(-234501570511346073600\) | \([2]\) | \(4423680\) | \(2.7545\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60690.f have rank \(0\).
Complex multiplication
The elliptic curves in class 60690.f do not have complex multiplication.Modular form 60690.2.a.f
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.