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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 153328o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 153328.l1 | 153328o1 | \([0, 0, 0, -13690, -455877]\) | \(6912000/1813\) | \(74426591672272\) | \([2]\) | \(306432\) | \(1.3705\) | \(\Gamma_0(N)\)-optimal |
| 153328.l2 | 153328o2 | \([0, 0, 0, 34225, -2937874]\) | \(6750000/9583\) | \(-6294363181426432\) | \([2]\) | \(612864\) | \(1.7171\) |
Rank
sage: E.rank()
The elliptic curves in class 153328o have rank \(0\).
Complex multiplication
The elliptic curves in class 153328o do not have complex multiplication.Modular form 153328.2.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.
