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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 55440.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.i1 | 55440cr4 | \([0, 0, 0, -307803, 65697802]\) | \(1080077156587801/594247500\) | \(1774413527040000\) | \([2]\) | \(393216\) | \(1.8741\) | |
| 55440.i2 | 55440cr2 | \([0, 0, 0, -22683, 633418]\) | \(432252699481/192099600\) | \(573606332006400\) | \([2, 2]\) | \(196608\) | \(1.5275\) | |
| 55440.i3 | 55440cr1 | \([0, 0, 0, -11163, -447158]\) | \(51520374361/887040\) | \(2648687247360\) | \([2]\) | \(98304\) | \(1.1809\) | \(\Gamma_0(N)\)-optimal |
| 55440.i4 | 55440cr3 | \([0, 0, 0, 78117, 4725898]\) | \(17655210697319/13448344140\) | \(-40156540428533760\) | \([2]\) | \(393216\) | \(1.8741\) |
Rank
sage: E.rank()
The elliptic curves in class 55440.i have rank \(1\).
Complex multiplication
The elliptic curves in class 55440.i do not have complex multiplication.Modular form 55440.2.a.i
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.
