Show commands:
SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 54450dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54450.w2 | 54450dg1 | \([1, -1, 0, 24828633, 7276364541]\) | \(3355354844375/1987172352\) | \(-1002488063082184800000000\) | \([]\) | \(7603200\) | \(3.2947\) | \(\Gamma_0(N)\)-optimal |
| 54450.w1 | 54450dg2 | \([1, -1, 0, -312080742, -2344283691084]\) | \(-6663170841705625/850403524608\) | \(-429011294045287219200000000\) | \([]\) | \(22809600\) | \(3.8440\) |
Rank
sage: E.rank()
The elliptic curves in class 54450dg have rank \(0\).
Complex multiplication
The elliptic curves in class 54450dg do not have complex multiplication.Modular form 54450.2.a.dg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
