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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 43758o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43758.t1 | 43758o1 | \([1, -1, 1, -15284, -392425]\) | \(14623266529962819/5950368579584\) | \(160659951648768\) | \([2]\) | \(155648\) | \(1.4236\) | \(\Gamma_0(N)\)-optimal |
| 43758.t2 | 43758o2 | \([1, -1, 1, 49996, -2899177]\) | \(511886728354194621/429557271832832\) | \(-11598046339486464\) | \([2]\) | \(311296\) | \(1.7701\) |
Rank
sage: E.rank()
The elliptic curves in class 43758o have rank \(1\).
Complex multiplication
The elliptic curves in class 43758o do not have complex multiplication.Modular form 43758.2.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.
