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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 103488.ii
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.ii1 | 103488io4 | \([0, 1, 0, -288526177, 1886269591583]\) | \(86129359107301290313/9166294368\) | \(282697496291136503808\) | \([2]\) | \(17694720\) | \(3.3520\) | |
| 103488.ii2 | 103488io2 | \([0, 1, 0, -18077537, 29315139615]\) | \(21184262604460873/216872764416\) | \(6688568471919783837696\) | \([2, 2]\) | \(8847360\) | \(3.0054\) | |
| 103488.ii3 | 103488io3 | \([0, 1, 0, -4530017, 72247230495]\) | \(-333345918055753/72923718045024\) | \(-2249038890081721667026944\) | \([2]\) | \(17694720\) | \(3.3520\) | |
| 103488.ii4 | 103488io1 | \([0, 1, 0, -2021217, -366573537]\) | \(29609739866953/15259926528\) | \(470631080550117408768\) | \([2]\) | \(4423680\) | \(2.6588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 103488.ii have rank \(1\).
Complex multiplication
The elliptic curves in class 103488.ii do not have complex multiplication.Modular form 103488.2.a.ii
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 LMFDB 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 LMFDB labels.
