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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 443760o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.o1 | 443760o1 | \([0, -1, 0, -592296, -140906880]\) | \(3550014724/725625\) | \(4697025599928960000\) | \([2]\) | \(8515584\) | \(2.2983\) | \(\Gamma_0(N)\)-optimal |
443760.o2 | 443760o2 | \([0, -1, 0, 1256704, -846485280]\) | \(16954370638/33698025\) | \(-436259737721401804800\) | \([2]\) | \(17031168\) | \(2.6449\) |
Rank
sage: E.rank()
The elliptic curves in class 443760o have rank \(0\).
Complex multiplication
The elliptic curves in class 443760o do not have complex multiplication.Modular form 443760.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.