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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 164730.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164730.o1 | 164730dl4 | \([1, 1, 0, -92018733608, -10743951557852352]\) | \(3569923749582532690899413792041/1088045913600\) | \(26262783314688038400\) | \([2]\) | \(429981696\) | \(4.4838\) | |
| 164730.o2 | 164730dl3 | \([1, 1, 0, -5751170088, -167876087041728]\) | \(-871563068987385209299047721/481164013657128960\) | \(-11614129579965892613898240\) | \([2]\) | \(214990848\) | \(4.1373\) | |
| 164730.o3 | 164730dl2 | \([1, 1, 0, -1136217233, -14733352773027]\) | \(6720696758719957188650041/4520567548335375000\) | \(109115511117105949203375000\) | \([2]\) | \(143327232\) | \(3.9345\) | |
| 164730.o4 | 164730dl1 | \([1, 1, 0, -57125913, -322951467483]\) | \(-854141175043560052921/1372088137570776000\) | \(-33118872094696098083544000\) | \([2]\) | \(71663616\) | \(3.5880\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 164730.o have rank \(0\).
Complex multiplication
The elliptic curves in class 164730.o do not have complex multiplication.Modular form 164730.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
