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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 152880ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.cr2 | 152880ct1 | \([0, -1, 0, 3120, -187200]\) | \(6967871/35100\) | \(-16914349670400\) | \([2]\) | \(414720\) | \(1.2205\) | \(\Gamma_0(N)\)-optimal |
| 152880.cr1 | 152880ct2 | \([0, -1, 0, -36080, -2351040]\) | \(10779215329/1232010\) | \(593693673431040\) | \([2]\) | \(829440\) | \(1.5671\) |
Rank
sage: E.rank()
The elliptic curves in class 152880ct have rank \(1\).
Complex multiplication
The elliptic curves in class 152880ct do not have complex multiplication.Modular form 152880.2.a.ct
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.
