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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 54080cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54080.f2 | 54080cr1 | \([0, 1, 0, -121, -441]\) | \(21952/5\) | \(44994560\) | \([2]\) | \(19968\) | \(0.18107\) | \(\Gamma_0(N)\)-optimal |
| 54080.f1 | 54080cr2 | \([0, 1, 0, -641, 5695]\) | \(405224/25\) | \(1799782400\) | \([2]\) | \(39936\) | \(0.52765\) |
Rank
sage: E.rank()
The elliptic curves in class 54080cr have rank \(1\).
Complex multiplication
The elliptic curves in class 54080cr do not have complex multiplication.Modular form 54080.2.a.cr
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.
