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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 52800di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.ed4 | 52800di1 | \([0, 1, 0, 67, 5763]\) | \(2048/891\) | \(-14256000000\) | \([2]\) | \(49152\) | \(0.62747\) | \(\Gamma_0(N)\)-optimal |
| 52800.ed3 | 52800di2 | \([0, 1, 0, -4433, 109263]\) | \(37642192/1089\) | \(278784000000\) | \([2, 2]\) | \(98304\) | \(0.97404\) | |
| 52800.ed2 | 52800di3 | \([0, 1, 0, -10433, -256737]\) | \(122657188/43923\) | \(44977152000000\) | \([2]\) | \(196608\) | \(1.3206\) | |
| 52800.ed1 | 52800di4 | \([0, 1, 0, -70433, 7171263]\) | \(37736227588/33\) | \(33792000000\) | \([2]\) | \(196608\) | \(1.3206\) |
Rank
sage: E.rank()
The elliptic curves in class 52800di have rank \(1\).
Complex multiplication
The elliptic curves in class 52800di do not have complex multiplication.Modular form 52800.2.a.di
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.
