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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5390.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5390.i1 | 5390c4 | \([1, -1, 0, -160066790, 779511027056]\) | \(3855131356812007128171561/8967612500\) | \(1055030643012500\) | \([2]\) | \(491520\) | \(3.0130\) | |
| 5390.i2 | 5390c3 | \([1, -1, 0, -10532510, 10824019800]\) | \(1098325674097093229481/205612182617187500\) | \(24190067672729492187500\) | \([2]\) | \(491520\) | \(3.0130\) | |
| 5390.i3 | 5390c2 | \([1, -1, 0, -10004290, 12181439556]\) | \(941226862950447171561/45393906250000\) | \(5340547676406250000\) | \([2, 2]\) | \(245760\) | \(2.6664\) | |
| 5390.i4 | 5390c1 | \([1, -1, 0, -592370, 211359700]\) | \(-195395722614328041/50730248800000\) | \(-5968363041071200000\) | \([2]\) | \(122880\) | \(2.3198\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5390.i have rank \(0\).
Complex multiplication
The elliptic curves in class 5390.i do not have complex multiplication.Modular form 5390.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
