Show commands:
SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 100800el
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.mk4 | 100800el1 | \([0, 0, 0, 18825, 14789500]\) | \(1012048064/130203045\) | \(-94918019805000000\) | \([2]\) | \(589824\) | \(1.9370\) | \(\Gamma_0(N)\)-optimal |
| 100800.mk3 | 100800el2 | \([0, 0, 0, -801300, 267388000]\) | \(1219555693504/43758225\) | \(2041583745600000000\) | \([2, 2]\) | \(1179648\) | \(2.2836\) | |
| 100800.mk2 | 100800el3 | \([0, 0, 0, -2016300, -736202000]\) | \(2428799546888/778248135\) | \(290479559892480000000\) | \([2]\) | \(2359296\) | \(2.6301\) | |
| 100800.mk1 | 100800el4 | \([0, 0, 0, -12708300, 17437282000]\) | \(608119035935048/826875\) | \(308629440000000000\) | \([2]\) | \(2359296\) | \(2.6301\) |
Rank
sage: E.rank()
The elliptic curves in class 100800el have rank \(1\).
Complex multiplication
The elliptic curves in class 100800el do not have complex multiplication.Modular form 100800.2.a.el
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
